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{{Task|Basic language learning}} {{basic data operation}} [[Category:Arithmetic operations]] [[Category:Mathematical_operations]] [[Category:Prime Numbers]]

;Task: Compute the [[wp:Divisor|factors]] of a positive integer.

These factors are the positive integers by which the number being factored can be divided to yield a positive integer result.

(Though the concepts function correctly for zero and negative integers, the set of factors of zero has countably infinite members, and the factors of negative integers can be obtained from the factors of related positive numbers without difficulty; this task does not require handling of either of these cases).

Note that every prime number has two factors: '''1''' and itself.

• [[count in factors]]
• [[prime decomposition]]
• [[Sieve of Eratosthenes]]
• [[primality by trial division]]
• [[factors of a Mersenne number]]
• [[trial factoring of a Mersenne number]]
• [[partition an integer X into N primes]]
• [[sequence of primes by Trial Division]]

}

print $(factors 36) {{out}} #(1 2 3 4 6 9 12 18 36) ## AutoHotkey msgbox, % factors(45) "n" factors(53) "n" factors(64) Factors(n) { Loop, % floor(sqrt(n)) { v := A_Index = 1 ? 1 "," n : mod(n,A_Index) ? v : v "," A_Index "," n//A_Index } Sort, v, N U D, Return, v } {{out}} 1,3,5,9,15,45 1,53 1,2,4,8,16,32,64 ## AutoIt ;AutoIt Version: 3.2.10.0$num = 45
MsgBox (0,"Factors", "Factors of " & $num & " are: " & factors($num))
consolewrite ("Factors of " & $num & " are: " & factors($num))
Func factors($intg)$ls_factors=""
For $i = 1 to$intg/2
if ($intg/$i - int($intg/$i))=0 Then
$ls_factors=$ls_factors&$i &", " EndIf Next Return$ls_factors&$intg EndFunc {{out}} Factors of 45 are: 1, 3, 5, 9, 15, 45 ## AWK # syntax: GAWK -f FACTORS_OF_AN_INTEGER.AWK BEGIN { print("enter a number or C/R to exit") } { if ($0 == "") { exit(0) }
if ($0 !~ /^[0-9]+$/) {
printf("invalid: %s\n",$0) next } n =$0
printf("factors of %s:",n)
for (i=1; i<=n; i++) {
if (n % i == 0) {
printf(" %d",i)
}
}
printf("\n")
}

{{out}}

enter a number or C/R to exit
invalid: -1
factors of 0:
factors of 1: 1
factors of 2: 1 2
factors of 11: 1 11
factors of 64: 1 2 4 8 16 32 64
factors of 100: 1 2 4 5 10 20 25 50 100
factors of 32766: 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766
factors of 32767: 1 7 31 151 217 1057 4681 32767

## BASIC

{{works with|QBasic}} This example stores the factors in a shared array (with the original number as the last element) for later retrieval.

Note that this will error out if you pass 32767 (or higher).

DECLARE SUB factor (what AS INTEGER)

REDIM SHARED factors(0) AS INTEGER

DIM i AS INTEGER, L AS INTEGER

INPUT "Gimme a number"; i

factor i

PRINT factors(0);
FOR L = 1 TO UBOUND(factors)
PRINT ","; factors(L);
NEXT
PRINT

SUB factor (what AS INTEGER)
DIM tmpint1 AS INTEGER
DIM L0 AS INTEGER, L1 AS INTEGER

REDIM tmp(0) AS INTEGER
REDIM factors(0) AS INTEGER
factors(0) = 1

FOR L0 = 2 TO what
IF (0 = (what MOD L0)) THEN
'all this REDIMing and copying can be replaced with:
'REDIM PRESERVE factors(UBOUND(factors)+1)
'in languages that support the PRESERVE keyword
REDIM tmp(UBOUND(factors)) AS INTEGER
FOR L1 = 0 TO UBOUND(factors)
tmp(L1) = factors(L1)
NEXT
REDIM factors(UBOUND(factors) + 1)
FOR L1 = 0 TO UBOUND(factors) - 1
factors(L1) = tmp(L1)
NEXT
factors(UBOUND(factors)) = L0
END IF
NEXT
END SUB

{{out}}

Gimme a number? 17
1 , 17
Gimme a number? 12345
1 , 3 , 5 , 15 , 823 , 2469 , 4115 , 12345
Gimme a number? 32765
1 , 5 , 6553 , 32765
Gimme a number? 32766
1 , 2 , 3 , 6 , 43 , 86 , 127 , 129 , 254 , 258 , 381 , 762 , 5461 , 10922 ,
16383 , 32766

==={{header|IS-BASIC}}=== 100 PROGRAM "Factors.bas" 110 INPUT PROMPT "Number: ":N 120 FOR I=1 TO INT(N/2) 130 IF MOD(N,I)=0 THEN PRINT I; 140 NEXT 150 PRINT N

=
## Sinclair ZX81 BASIC
=

basic
10 INPUT N
20 FOR I=1 TO N
30 IF N/I=INT (N/I) THEN PRINT I;" ";
40 NEXT I

{{in}}

315

{{out}}

1 3 5 7 9 15 35 45 63 105 315

## Batch File

Command line version:

@echo off
set res=Factors of %1:
for /L %%i in (1,1,%1) do call :fac %1 %%i
echo %res%
goto :eof

:fac
set /a test = %1 %% %2
if %test% equ 0 set res=%res% %2

{{out}}

>factors 32767
Factors of 32767: 1 7 31 151 217 1057 4681 32767

>factors 45
Factors of 45: 1 3 5 9 15 45

>factors 53
Factors of 53: 1 53

>factors 64
Factors of 64: 1 2 4 8 16 32 64

>factors 100
Factors of 100: 1 2 4 5 10 20 25 50 100

Interactive version:

@echo off
set /p limit=Gimme a number:
set res=Factors of %limit%:
for /L %%i in (1,1,%limit%) do call :fac %limit% %%i
echo %res%
goto :eof

:fac
set /a test = %1 %% %2
if %test% equ 0 set res=%res% %2

{{out}}

>factors
Gimme a number:27
Factors of 27: 1 3 9 27

>factors
Gimme a number:102
Factors of 102: 1 2 3 6 17 34 51 102

## BBC BASIC

{{works with|BBC BASIC for Windows}}

INSTALL @lib$+"SORTLIB" sort% = FN_sortinit(0, 0) PRINT "The factors of 45 are " FNfactorlist(45) PRINT "The factors of 12345 are " FNfactorlist(12345) END DEF FNfactorlist(N%) LOCAL C%, I%, L%(), L$
DIM L%(32)
FOR I% = 1 TO SQR(N%)
IF (N% MOD I% = 0) THEN
L%(C%) = I%
C% += 1
IF (N% <> I%^2) THEN
L%(C%) = (N% DIV I%)
C% += 1
ENDIF
ENDIF
NEXT I%
CALL sort%, L%(0)
FOR I% = 0 TO C%-1
L$+= STR$(L%(I%)) + ", "
NEXT
= LEFT$(LEFT$(L$)) {{out}} The factors of 45 are 1, 3, 5, 9, 15, 45 The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345 ## bc /* Calculate the factors of n and return their count. * This function mutates the global array f[] which will * contain all factors of n in ascending order after the call! */ define f(n) { auto i, d, h, h[], l, o /* Local variables: * i: Loop variable. * d: Complementary (higher) factor to i. * h: Will always point to the last element of h[]. * h[]: Array to hold the greater factor of the pair (x, y), where * x * y == n. The factors are stored in descending order. * l: Will always point to the next free spot in f[]. * o: For saving the value of scale. */ /* Use integer arithmetic */ o = scale scale = 0 /* Two factors are 1 and n (if n != 1) */ f[l++] = 1 if (n == 1) return(1) h[0] = n /* Main loop */ for (i = 2; i < h[h]; i++) { if (n % i == 0) { d = n / i if (d != i) { h[++h] = d } f[l++] = i } } /* Append the values in h[] to f[] */ while (h >= 0) { f[l++] = h[h--] } scale = o return(l) } ## Befunge 10:p&v: >:0:g%#v_0:g\:0:g/\v >:0:g:*| > >0:g1+0:p >:0:g:*-#v_0:g\>$>:!#@_.v
>     ^ ^  ," "<

## Burlesque

blsq ) 32767 fc
{1 7 31 151 217 1057 4681 32767}

## C

#include <stdio.h>
#include <stdlib.h>

typedef struct {
int *list;
short count;
} Factors;

void xferFactors( Factors *fctrs, int *flist, int flix )
{
int ix, ij;
int newSize = fctrs->count + flix;
if (newSize > flix)  {
fctrs->list = realloc( fctrs->list, newSize * sizeof(int));
}
else {
fctrs->list = malloc(  newSize * sizeof(int));
}
for (ij=0,ix=fctrs->count; ix<newSize; ij++,ix++) {
fctrs->list[ix] = flist[ij];
}
fctrs->count = newSize;
}

Factors *factor( int num, Factors *fctrs)
{
int flist[301], flix;
int dvsr;
flix = 0;
fctrs->count = 0;
free(fctrs->list);
fctrs->list = NULL;
for (dvsr=1; dvsr*dvsr < num; dvsr++) {
if (num % dvsr != 0) continue;
if ( flix == 300) {
xferFactors( fctrs, flist, flix );
flix = 0;
}
flist[flix++] = dvsr;
flist[flix++] = num/dvsr;
}
if (dvsr*dvsr == num)
flist[flix++] = dvsr;
if (flix > 0)
xferFactors( fctrs, flist, flix );

return fctrs;
}

int main(int argc, char*argv[])
{
int nums2factor[] = { 2059, 223092870, 3135, 45 };
Factors ftors = { NULL, 0};
char sep;
int i,j;

for (i=0; i<4; i++) {
factor( nums2factor[i], &ftors );
printf("\nfactors of %d are:\n  ", nums2factor[i]);
sep = ' ';
for (j=0; j<ftors.count; j++) {
printf("%c %d", sep, ftors.list[j]);
sep = ',';
}
printf("\n");
}
return 0;
}

### Prime factoring

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* 65536 = 2^16, so we can factor all 32 bit ints */
char bits[65536];

typedef unsigned long ulong;
ulong primes[7000], n_primes;

typedef struct { ulong p, e; } prime_factor; /* prime, exponent */

void sieve()
{
int i, j;
memset(bits, 1, 65536);
bits[0] = bits[1] = 0;
for (i = 0; i < 256; i++)
if (bits[i])
for (j = i * i; j < 65536; j += i)
bits[j] = 0;

/* collect primes into a list. slightly faster this way if dealing with large numbers */
for (i = j = 0; i < 65536; i++)
if (bits[i]) primes[j++] = i;

n_primes = j;
}

int get_prime_factors(ulong n, prime_factor *lst)
{
ulong i, e, p;
int len = 0;

for (i = 0; i < n_primes; i++) {
p = primes[i];
if (p * p > n) break;
for (e = 0; !(n % p); n /= p, e++);
if (e) {
lst[len].p = p;
lst[len++].e = e;
}
}

return n == 1 ? len : (lst[len].p = n, lst[len].e = 1, ++len);
}

int ulong_cmp(const void *a, const void *b)
{
return *(const ulong*)a < *(const ulong*)b ? -1 : *(const ulong*)a > *(const ulong*)b;
}

int get_factors(ulong n, ulong *lst)
{
int n_f, len, len2, i, j, k, p;
prime_factor f[100];

n_f = get_prime_factors(n, f);

len2 = len = lst[0] = 1;
/* L = (1); L = (L, L * p**(1 .. e)) forall((p, e)) */
for (i = 0; i < n_f; i++, len2 = len)
for (j = 0, p = f[i].p; j < f[i].e; j++, p *= f[i].p)
for (k = 0; k < len2; k++)
lst[len++] = lst[k] * p;

qsort(lst, len, sizeof(ulong), ulong_cmp);
return len;
}

int main()
{
ulong fac[10000];
int len, i, j;
ulong nums[] = {3, 120, 1024, 2UL*2*2*2*3*3*3*5*5*7*11*13*17*19 };

sieve();

for (i = 0; i < 4; i++) {
len = get_factors(nums[i], fac);
printf("%lu:", nums[i]);
for (j = 0; j < len; j++)
printf(" %lu", fac[j]);
printf("\n");
}

return 0;
}

{{out}}

3: 1 3
120: 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
1024: 1 2 4 8 16 32 64 128 256 512 1024
3491888400: 1 2 3 4 5 6 7 8 9 10 11 ...(>1900 numbers)... 1163962800 1745944200 3491888400

## C++

#include <iostream>
#include <vector>
#include <algorithm>
#include <iterator>

std::vector<int> GenerateFactors(int n)
{
std::vector<int> factors;
factors.push_back(1);
factors.push_back(n);
for(int i = 2; i * i <= n; ++i)
{
if(n % i == 0)
{
factors.push_back(i);
if(i * i != n)
factors.push_back(n / i);
}
}

std::sort(factors.begin(), factors.end());
return factors;
}

int main()
{
const int SampleNumbers[] = {3135, 45, 60, 81};

for(size_t i = 0; i < sizeof(SampleNumbers) / sizeof(int); ++i)
{
std::vector<int> factors = GenerateFactors(SampleNumbers[i]);
std::cout << "Factors of " << SampleNumbers[i] << " are:\n";
std::copy(factors.begin(), factors.end(), std::ostream_iterator<int>(std::cout, "\n"));
std::cout << std::endl;
}
}

## C#

C# 3.0

using System;
using System.Linq;
using System.Collections.Generic;

public static class Extension
{
public static List<int> Factors(this int me)
{
return Enumerable.Range(1, me).Where(x => me % x == 0).ToList();
}
}

class Program
{
static void Main(string[] args)
{
Console.WriteLine(String.Join(", ", 45.Factors()));
}
}

C# 1.0

static void Main(string[] args)
{
do
{
Console.WriteLine("Number:");
Int64 p = 0;
do
{
try
{
break;
}
catch (Exception)
{ }

} while (true);

Console.WriteLine("For 1 through " + ((int)Math.Sqrt(p)).ToString() + "");
for (int x = 1; x <= (int)Math.Sqrt(p); x++)
{
if (p % x == 0)
Console.WriteLine("Found: " + x.ToString() + ". " + p.ToString() + " / " + x.ToString() + " = " + (p / x).ToString());
}

Console.WriteLine("Done.");
} while (true);
}

{{out}}

Number:
32434243
For 1 through 5695
Found: 1. 32434243 / 1 = 32434243
Found: 307. 32434243 / 307 = 105649
Done.

## Ceylon

shared void run() {
{Integer*} getFactors(Integer n) =>
(1..n).filter((Integer element) => element.divides(n));

for(Integer i in 1..100) {
print("the factors of i are getFactors(i)");
}
}

## Chapel

Inspired by the Clojure solution:

iter factors(n) {
for i in 1..floor(sqrt(n)):int {
if n % i == 0 then {
yield i;
yield n / i;
}
}
}

## Clojure

(defn factors [n]
(filter #(zero? (rem n %)) (range 1 (inc n))))

(print (factors 45))

(1 3 5 9 15 45)

Improved version. Considers small factors from 1 up to (sqrt n) -- we increment it because range does not include the end point. Pair each small factor with its co-factor, flattening the results, and put them into a sorted set to get the factors in order.

(defn factors [n]
(into (sorted-set)
(mapcat (fn [x] [x (/ n x)])
(filter #(zero? (rem n %)) (range 1 (inc (Math/sqrt n)))) )))

Same idea, using for comprehensions.

(defn factors [n]
(into (sorted-set)
(reduce concat
(for [x (range 1 (inc (Math/sqrt n))) :when (zero? (rem n x))]
[x (/ n x)]))))

## COBOL

IDENTIFICATION DIVISION.
PROGRAM-ID. FACTORS.
DATA DIVISION.
WORKING-STORAGE SECTION.
01  CALCULATING.
03  NUM  USAGE BINARY-LONG VALUE ZERO.
03  LIM  USAGE BINARY-LONG VALUE ZERO.
03  CNT  USAGE BINARY-LONG VALUE ZERO.
03  DIV  USAGE BINARY-LONG VALUE ZERO.
03  REM  USAGE BINARY-LONG VALUE ZERO.
03  ZRS  USAGE BINARY-SHORT VALUE ZERO.

01  DISPLAYING.
03  DIS  PIC 9(10) USAGE DISPLAY.

PROCEDURE DIVISION.
MAIN-PROCEDURE.
DISPLAY "Factors of? " WITH NO ADVANCING
ACCEPT NUM
DIVIDE NUM BY 2 GIVING LIM.

PERFORM VARYING CNT FROM 1 BY 1 UNTIL CNT > LIM
DIVIDE NUM BY CNT GIVING DIV REMAINDER REM
IF REM = 0
MOVE CNT TO DIS
PERFORM SHODIS
END-IF
END-PERFORM.

MOVE NUM TO DIS.
PERFORM SHODIS.
STOP RUN.

SHODIS.
MOVE ZERO TO ZRS.
INSPECT DIS TALLYING ZRS FOR LEADING ZERO.
DISPLAY DIS(ZRS + 1:)
EXIT PARAGRAPH.

END PROGRAM FACTORS.

## CoffeeScript

# Reference implementation for finding factors is slow, but hopefully
# robust--we'll use it to verify the more complicated (but hopefully faster)
# algorithm.
slow_factors = (n) ->
(i for i in [1..n] when n % i == 0)

# The rest of this code does two optimizations:
#   1) When you find a prime factor, divide it out of n (smallest_prime_factor).
#   2) Find the prime factorization first, then compute composite factors from those.

smallest_prime_factor = (n) ->
for i in [2..n]
return n if i*i > n
return i if n % i == 0

prime_factors = (n) ->
return {} if n == 1
spf = smallest_prime_factor n
result = prime_factors(n / spf)
result[spf] or= 0
result[spf] += 1
result

fast_factors = (n) ->
prime_hash = prime_factors n
exponents = []
for p of prime_hash
exponents.push
p: p
exp: 0
result = []
while true
factor = 1
for obj in exponents
factor *= Math.pow obj.p, obj.exp
result.push factor
break if factor == n
# roll the odometer
for obj, i in exponents
if obj.exp < prime_hash[obj.p]
obj.exp += 1
break
else
obj.exp = 0

return result.sort (a, b) -> a - b

verify_factors = (factors, n) ->
expected_result = slow_factors n
throw Error("wrong length") if factors.length != expected_result.length
for factor, i in expected_result
console.log Error("wrong value") if factors[i] != factor

for n in [1, 3, 4, 8, 24, 37, 1001, 11111111111, 99999999999]
factors = fast_factors n
console.log n, factors
if n < 1000000
verify_factors factors, n

{{out}}

> coffee factors.coffee
1 [ 1 ]
3 [ 1, 3 ]
4 [ 1, 2, 4 ]
8 [ 1, 2, 4, 8 ]
24 [ 1, 2, 3, 4, 6, 8, 12, 24 ]
37 [ 1, 37 ]
1001 [ 1, 7, 11, 13, 77, 91, 143, 1001 ]
11111111111 [ 1, 21649, 513239, 11111111111 ]
99999999999 [ 1,
3,
9,
21649,
64947,
194841,
513239,
1539717,
4619151,
11111111111,
33333333333,
99999999999 ]

## Common Lisp

We iterate in the range 1..sqrt(n) collecting ‘low’ factors and corresponding ‘high’ factors, and combine at the end to produce an ordered list of factors.

(defun factors (n &aux (lows '()) (highs '()))
(do ((limit (1+ (isqrt n))) (factor 1 (1+ factor)))
((= factor limit)
(when (= n (* limit limit))
(push limit highs))
(remove-duplicates (nreconc lows highs)))
(multiple-value-bind (quotient remainder) (floor n factor)
(when (zerop remainder)
(push factor lows)
(push quotient highs)))))

## D

### Procedural Style

import std.stdio, std.math, std.algorithm;

T[] factors(T)(in T n) pure nothrow {
if (n == 1)
return [n];

T[] res = [1, n];
T limit = cast(T)real(n).sqrt + 1;
for (T i = 2; i < limit; i++) {
if (n % i == 0) {
res ~= i;
immutable q = n / i;
if (q > i)
res ~= q;
}
}

return res.sort().release;
}

void main() {
writefln("%(%s\n%)", [45, 53, 64, 1111111].map!factors);
}

{{out}}

[1, 3, 5, 9, 15, 45]
[1, 53]
[1, 2, 4, 8, 16, 32, 64]
[1, 239, 4649, 1111111]

### Functional Style

import std.stdio, std.algorithm, std.range;

auto factors(I)(I n) {
return iota(1, n + 1).filter!(i => n % i == 0);
}

void main() {
36.factors.writeln;
}

{{out}}

[1, 2, 3, 4, 6, 9, 12, 18, 36]

## Dart

import 'dart:math';

factors(n)
{
var factorsArr = [];
for(var test = n - 1; test >= sqrt(n).toInt(); test--)
if(n % test == 0)
{
}
return factorsArr;
}

void main() {
print(factors(5688));
}

## Dyalect

func Iterator.where(pred) {
for x in this when pred(x) {
yield x
}
}

func Integer.factors() {
(1..this).where(this % $0 == 0) } for x in 45.factors() { print(x) } Output: 1 3 5 9 15 45 ## E {{improve|E|Use a cleverer algorithm such as in the Common Lisp example.}} def factors(x :(int > 0)) { var xfactors := [] for f ? (x % f <=> 0) in 1..x { xfactors with= f } return xfactors } ## EasyLang n = 720 for i = 1 to n if n mod i = 0 factors[] &= i . . print factors[] ## EchoLisp '''prime-factors''' gives the list of n's prime-factors. We mix them to get all the factors. scheme ;; ppows ;; input : a list g of grouped prime factors ( 3 3 3 ..) ;; returns (1 3 9 27 ...) (define (ppows g (mult 1)) (for/fold (ppows '(1)) ((a g)) (set! mult (* mult a)) (cons mult ppows))) ;; factors ;; decomp n into ((2 2 ..) ( 3 3 ..) ) prime factors groups ;; combines (1 2 4 8 ..) (1 3 9 ..) lists (define (factors n) (list-sort < (if (<= n 1) '(1) (for/fold (divs'(1)) ((g (map ppows (group (prime-factors n))))) (for*/list ((a divs) (b g)) (* a b)))))) {{out}} (lib 'bigint) (factors 666) → (1 2 3 6 9 18 37 74 111 222 333 666) (length (factors 108233175859200)) → 666 ;; 💀 (define huge 1200034005600070000008900000000000000000) (time ( length (factors huge))) → (394ms 7776) ## Ela ===Using higher-order function=== open list factors m = filter (\x -> m % x == 0) [1..m] ### Using comprehension factors m = [x \\ x <- [1..m] | m % x == 0] ## Elixir defmodule RC do def factor(1), do: [1] def factor(n) do (for i <- 1..div(n,2), rem(n,i)==0, do: i) ++ [n] end # Recursive (faster version); def divisor(n), do: divisor(n, 1, []) |> Enum.sort defp divisor(n, i, factors) when n < i*i , do: factors defp divisor(n, i, factors) when n == i*i , do: [i | factors] defp divisor(n, i, factors) when rem(n,i)==0, do: divisor(n, i+1, [i, div(n,i) | factors]) defp divisor(n, i, factors) , do: divisor(n, i+1, factors) end Enum.each([45, 53, 60, 64], fn n -> IO.puts "#{n}: #{inspect RC.factor(n)}" end) IO.puts "\nRange: #{inspect range = 1..10000}" funs = [ factor: &RC.factor/1, divisor: &RC.divisor/1 ] Enum.each(funs, fn {name, fun} -> {time, value} = :timer.tc(fn -> Enum.count(range, &length(fun.(&1))==2) end) IO.puts "#{name}\t prime count : #{value},\t#{time/1000000} sec" end) {{out}} 45: [1, 3, 5, 9, 15, 45] 53: [1, 53] 60: [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] 64: [1, 2, 4, 8, 16, 32, 64] Range: 1..10000 factor prime count : 1229, 7.316 sec divisor prime count : 1229, 0.265 sec ## Erlang ### with Built in fuctions factors(N) -> [I || I <- lists:seq(1,trunc(N/2)), N rem I == 0]++[N]. ### Recursive Another, less concise, but faster version -module(divs). -export([divs/1]). divs(0) -> []; divs(1) -> []; divs(N) -> lists:sort(divisors(1,N))++[N]. divisors(1,N) -> [1] ++ divisors(2,N,math:sqrt(N)). divisors(K,_N,Q) when K > Q -> []; divisors(K,N,_Q) when N rem K =/= 0 -> [] ++ divisors(K+1,N,math:sqrt(N)); divisors(K,N,_Q) when K * K == N -> [K] ++ divisors(K+1,N,math:sqrt(N)); divisors(K,N,_Q) -> [K, N div K] ++ divisors(K+1,N,math:sqrt(N)). {{out}} 58> timer:tc(divs, factors, [20000]). {2237, [1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400, 500,625,800,1000,1250,2000,2500,4000|...]} 59> timer:tc(divs, divs, [20000]). {106, [1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400, 500,625,800,1000,1250,2000,2500,4000|...]} The first number is milliseconds. I'v ommitted repeating the first fuction. ## ERRE PROGRAM FACTORS !$DOUBLE

PROCEDURE FACTORLIST(N->L$) LOCAL C%,I,FLIPS%,I% LOCAL DIM L[32] FOR I=1 TO SQR(N) DO IF N=I*INT(N/I) THEN L[C%]=I C%=C%+1 IF N<>I*I THEN L[C%]=INT(N/I) C%=C%+1 END IF END IF END FOR ! BUBBLE SORT ARRAY L[] FLIPS%=1 WHILE FLIPS%>0 DO FLIPS%=0 FOR I%=0 TO C%-2 DO IF L[I%]>L[I%+1] THEN SWAP(L[I%],L[I%+1]) FLIPS%=1 END FOR END WHILE L$=""
FOR I%=0 TO C%-1 DO
L$=L$+STR$(L[I%])+"," END FOR L$=LEFT$(L$,LEN(L$)-1) END PROCEDURE BEGIN PRINT(CHR$(12);) ! CLS
FACTORLIST(45->L$) PRINT("The factors of 45 are ";L$)
FACTORLIST(12345->L$) PRINT("The factors of 12345 are ";L$)
END PROGRAM

{{out}}

The factors of 45 are  1, 3, 5, 9, 15, 45
The factors of 12345 are  1, 3, 5, 15, 823, 2469, 4115, 12345

=={{header|F Sharp|F#}}== If number % divisor = 0 then both divisor AND number / divisor are factors.

So, we only have to search till sqrt(number).

Also, this is lazily evaluated.

let factors number = seq {
for divisor in 1 .. (float >> sqrt >> int) number do
if number % divisor = 0 then
yield divisor
if number <> 1 then yield number / divisor //special case condition: when number=1 then divisor=(number/divisor), so don't repeat it
}

### Prime factoring

[6;120;2048;402642;1206432] |> Seq.iter(fun n->printf "%d :" n; [1..n]|>Seq.filter(fun g->n%g=0)|>Seq.iter(fun n->printf " %d" n); printfn "");;

{{out}}

OUTPUT :
6 : 1  2  3  6
120 : 1  2  3  4  5  6  8  10  12  15  20  24  30  40  60  120
2048 : 1  2  4  8  16  32  64  128  256  512  1024  2048
402642 : 1  2  3  6  9  18  22369  44738  67107  134214  201321  402642
120643200 : 1  2  3  4  6  8  9  12  16  18  24  32  36  48  59  71  72  96  118  142  144  177  213  236  284  288  354  426  472  531  568  639  708  852  944  1062  1136  12
78  1416  1704  1888  2124  2272  2556  2832  3408  4189  4248  5112  5664  6816  8378  8496  10224  12567  16756  16992  20448  25134  33512  37701  50268  67024  75402  10053
6  134048  150804  201072  301608  402144  603216  1206432

=={{Header|Factor}}== USE: math.primes.factors ( scratchpad ) 24 divisors . { 1 2 3 4 6 8 12 24 }

else
factorStr = factorStr + str$(l(i)) end if next end fn = factorStr print "Factors of 25 are:"; fn IntegerFactors( 25 ) print "Factors of 45 are:"; fn IntegerFactors( 45 ) print "Factors of 103 are:"; fn IntegerFactors( 103 ) print "Factors of 760 are:"; fn IntegerFactors( 760 ) print "Factors of 12345 are:"; fn IntegerFactors( 12345 ) print "Factors of 32766 are:"; fn IntegerFactors( 32766 ) print "Factors of 32767 are:"; fn IntegerFactors( 32767 ) print "Factors of 57097 are:"; fn IntegerFactors( 57097 ) print "Factors of 12345678 are:"; fn IntegerFactors( 12345678 ) print "Factors of 32434243 are:"; fn IntegerFactors( 32434243 ) Output: Factors of 25 are: 1, 5, 25 Factors of 45 are: 1, 3, 5, 9, 15, 45 Factors of 103 are: 1, 103 Factors of 760 are: 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760 Factors of 12345 are: 1, 3, 5, 15, 823, 2469, 4115, 12345 Factors of 32766 are: 1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766 Factors of 32767 are: 1, 7, 31, 151, 217, 1057, 4681, 32767 Factors of 57097 are: 1, 57097 Factors of 12345678 are: 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 14593, 29186, 43779, 87558, 131337, 262674, 685871, 1371742, 2057613, 4115226, 6172839, 12345678 Factors of 32434243 are: 1, 307, 105649, 32434243 ## GAP # Built-in function DivisorsInt(Factorial(5)); # [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ] # A possible implementation, not suitable to large n div := n -> Filtered([1 .. n], k -> n mod k = 0); div(Factorial(5)); # [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ] # Another implementation, usable for large n (if n can be factored quickly) div2 := function(n) local f, p; f := Collected(FactorsInt(n)); p := List(f, v -> List([0 .. v[2]], k -> v[1]^k)); return SortedList(List(Cartesian(p), Product)); end; div2(Factorial(5)); # [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ] ## Go Trial division, no prime number generator, but with some optimizations. It's good enough to factor any 64 bit integer, with large primes taking several seconds. package main import "fmt" func main() { printFactors(-1) printFactors(0) printFactors(1) printFactors(2) printFactors(3) printFactors(53) printFactors(45) printFactors(64) printFactors(600851475143) printFactors(999999999999999989) } func printFactors(nr int64) { if nr < 1 { fmt.Println("\nFactors of", nr, "not computed") return } fmt.Printf("\nFactors of %d: ", nr) fs := make([]int64, 1) fs[0] = 1 apf := func(p int64, e int) { n := len(fs) for i, pp := 0, p; i < e; i, pp = i+1, pp*p { for j := 0; j < n; j++ { fs = append(fs, fs[j]*pp) } } } e := 0 for ; nr & 1 == 0; e++ { nr >>= 1 } apf(2, e) for d := int64(3); nr > 1; d += 2 { if d*d > nr { d = nr } for e = 0; nr%d == 0; e++ { nr /= d } if e > 0 { apf(d, e) } } fmt.Println(fs) fmt.Println("Number of factors =", len(fs)) } {{out}} Factors of -1 not computed Factors of 0 not computed Factors of 1: [1] Number of factors = 1 Factors of 2: [1 2] Number of factors = 2 Factors of 3: [1 3] Number of factors = 2 Factors of 53: [1 53] Number of factors = 2 Factors of 45: [1 3 9 5 15 45] Number of factors = 6 Factors of 64: [1 2 4 8 16 32 64] Number of factors = 7 Factors of 600851475143: [1 71 839 59569 1471 104441 1234169 87625999 6857 486847 5753023 408464633 10086647 716151937 8462696833 600851475143] Number of factors = 16 Factors of 999999999999999989: [1 999999999999999989] Number of factors = 2 ## Gosu var numbers = {11, 21, 32, 45, 67, 96} numbers.each(\ number -> printFactors(number)) function printFactors(n: int) { if (n < 1) return var result ="${n} => "
(1 .. n/2).each(\ i -> {result += n % i == 0 ? "${i} " : ""}) print("${result}${n}") } {{out}} 11 => 1 11 21 => 1 3 7 21 32 => 1 2 4 8 16 32 45 => 1 3 5 9 15 45 67 => 1 67 96 => 1 2 3 4 6 8 12 16 24 32 48 96 =={{Header|Groovy}}== A straight brute force approach up to the square root of ''N'': def factorize = { long target -> if (target == 1) return [1L] if (target < 4) return [1L, target] def targetSqrt = Math.sqrt(target) def lowfactors = (2L..targetSqrt).grep { (target % it) == 0 } if (lowfactors == []) return [1L, target] def nhalf = lowfactors.size() - ((lowfactors[-1] == targetSqrt) ? 1 : 0) [1] + lowfactors + (0..<nhalf).collect { target.intdiv(lowfactors[it]) }.reverse() + [target] } Test: ((1..30) + [333333]).each { println ([number:it, factors:factorize(it)]) } {{out}} [number:1, factors:[1]] [number:2, factors:[1, 2]] [number:3, factors:[1, 3]] [number:4, factors:[1, 2, 4]] [number:5, factors:[1, 5]] [number:6, factors:[1, 2, 3, 6]] [number:7, factors:[1, 7]] [number:8, factors:[1, 2, 4, 8]] [number:9, factors:[1, 3, 9]] [number:10, factors:[1, 2, 5, 10]] [number:11, factors:[1, 11]] [number:12, factors:[1, 2, 3, 4, 6, 12]] [number:13, factors:[1, 13]] [number:14, factors:[1, 2, 7, 14]] [number:15, factors:[1, 3, 5, 15]] [number:16, factors:[1, 2, 4, 8, 16]] [number:17, factors:[1, 17]] [number:18, factors:[1, 2, 3, 6, 9, 18]] [number:19, factors:[1, 19]] [number:20, factors:[1, 2, 4, 5, 10, 20]] [number:21, factors:[1, 3, 7, 21]] [number:22, factors:[1, 2, 11, 22]] [number:23, factors:[1, 23]] [number:24, factors:[1, 2, 3, 4, 6, 8, 12, 24]] [number:25, factors:[1, 5, 25]] [number:26, factors:[1, 2, 13, 26]] [number:27, factors:[1, 3, 9, 27]] [number:28, factors:[1, 2, 4, 7, 14, 28]] [number:29, factors:[1, 29]] [number:30, factors:[1, 2, 3, 5, 6, 10, 15, 30]] [number:333333, factors:[1, 3, 7, 9, 11, 13, 21, 33, 37, 39, 63, 77, 91, 99, 111, 117, 143, 231, 259, 273, 333, 407, 429, 481, 693, 777, 819, 1001, 1221, 1287, 1443, 2331, 2849, 3003, 3367, 3663, 4329, 5291, 8547, 9009, 10101, 15873, 25641, 30303, 37037, 47619, 111111, 333333]] =={{Header|Haskell}}== Using [https://web.archive.org/web/20121130222921/http://www.polyomino.f2s.com/david/haskell/codeindex.html D. Amos'es Primes module] for finding prime factors import HFM.Primes (primePowerFactors) import Control.Monad (mapM) import Data.List (product) -- primePowerFactors :: Integer -> [(Integer,Int)] factors = map product . mapM (\(p,m)-> [p^i | i<-[0..m]]) . primePowerFactors Returns list of factors out of order, e.g.: ~> factors 42 [1,7,3,21,2,14,6,42] Or, [[Prime_decomposition#Haskell|prime decomposition task]] can be used (although, a trial division-only version will become very slow for large primes), haskell import Data.List (group) primePowerFactors = map (\x-> (head x, length x)) . group . factorize The above function can also be found in the package [http://hackage.haskell.org/package/arithmoi arithmoi], as Math.NumberTheory.Primes.factorise :: Integer -> [(Integer, Int)], [http://hackage.haskell.org/package/arithmoi-0.4.2.0/docs/Math-NumberTheory-Primes-Factorisation.html which performs] "factorisation of Integers by the elliptic curve algorithm after Montgomery" and "is best suited for numbers of up to 50-60 digits". Or, deriving cofactors from factors up to the square root: import Control.Arrow ((&&&)) import Data.Bool (bool) integerFactors :: Int -> [Int] integerFactors n = bool -- For perfect squares, tail excludes cofactor of square root (lows ++ (quot n <$> bool id tail (n == intSquared) (reverse lows)))
[]
(n < 1)
where
(intSquared, lows) =
(^ 2) &&& (filter ((0 ==) . rem n) . enumFromTo 1) $floor (sqrt$ fromIntegral n)

main :: IO ()
main = print integerFactors 600 {{Out}} [1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600] ### List comprehension Naive, functional, no import, in increasing order: factorsNaive n = [ i | i <- [1 .. n] , mod n i == 0 ] ~> factorsNaive 25 [1,5,25] Factor, ''cofactor''. Get the list of factor–cofactor pairs sorted, for a quadratic speedup: import Data.List (sort) factorsCo n = sort [ i | i <- [1 .. floor (sqrt (fromIntegral n))] , (d, 0) <- [divMod n i] , i <- i : [ d | d > i ] ] A version of the above without the need for sorting, making it to be ''online'' (i.e. productive immediately, which can be seen in GHCi); factors in increasing order: factorsO n = ds ++ [ r | (d, 0) <- [divMod n r] , r <- r : [ d | d > r ] ] ++ reverse (map (n div) ds) where r = floor (sqrt (fromIntegral n)) ds = [ i | i <- [1 .. r - 1] , mod n i == 0 ] Testing: *Main> :set +s ~> factorsO 120 [1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120] (0.00 secs, 0 bytes) ~> factorsO 12041111117 [1,7,41,287,541,3787,22181,77551,155267,542857,3179591,22257137,41955091,2936856 37,1720158731,12041111117] (0.09 secs, 50758224 bytes) ## HicEst DLG(NameEdit=N, TItle='Enter an integer') DO i = 1, N^0.5 IF( MOD(N,i) == 0) WRITE() i, N/i ENDDO END =={{header|Icon}} and {{header|Unicon}}== procedure main(arglist) numbers := arglist ||| [ 32767, 45, 53, 64, 100] # combine command line provided and default set of values every writes(lf,"factors of ",i := !numbers,"=") & writes(divisors(i)," ") do lf := "\n" end link factors {{out}} factors of 32767=1 7 31 151 217 1057 4681 32767 factors of 45=1 3 5 9 15 45 factors of 53=1 53 factors of 64=1 2 4 8 16 32 64 factors of 100=1 2 4 5 10 20 25 50 100 {{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/factors.icn divisors] ## J The "brute force" approach is the most concise: foi=: [: I. 0 = (|~ i.@>:) Example use: foi 40 1 2 4 5 8 10 20 40 Basically we test every non-negative integer up through the number itself to see if it divides evenly. However, this becomes very slow for large numbers. So other approaches can be worthwhile. J has a primitive, q: which returns its argument's prime factors. q: 40 2 2 2 5 Alternatively, q: can produce provide a table of the exponents of the unique relevant prime factors __ q: 420 2 3 5 7 2 1 1 1 With this, we can form lists of each of the potential relevant powers of each of these prime factors (^ i.@>:)&.>/ __ q: 420 ┌─────┬───┬───┬───┐ │1 2 4│1 3│1 5│1 7│ └─────┴───┴───┴───┘ From here, it's a simple matter (*/&>@{) to compute all possible factors of the original number factrs=: */&>@{@((^ i.@>:)&.>/)@q:~&__ factrs 40 1 5 2 10 4 20 8 40 However, a data structure which is organized around the prime decomposition of the argument can be hard to read. So, for reader convenience, we should probably arrange them in a monotonically increasing list: factors=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__ factors 420 1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 140 210 420 A less efficient, but concise variation on this theme: ~.,*/&> { 1 ,&.> q: 40 1 5 2 10 4 20 8 40 This computes 2^n intermediate values where n is the number of prime factors of the original number. That said, note that we get a representation issue when dealing with large numbers: factors 568474220 1 2 4 5 10 17 20 34 68 85 170 340 1.67198e6 3.34397e6 6.68793e6 8.35992e6 1.67198e7 2.84237e7 3.34397e7 5.68474e7 1.13695e8 1.42119e8 2.84237e8 5.68474e8 One approach here (if we don't want to explicitly format the result) is to use an arbitrary precision (aka "extended") argument. This propagates through into the result: factors 568474220x 1 2 4 5 10 17 20 34 68 85 170 340 1671983 3343966 6687932 8359915 16719830 28423711 33439660 56847422 113694844 142118555 284237110 568474220 Another less efficient approach, in which remainders are examined up to the square root, larger factors obtained as fractions, and the combined list nubbed and sorted might be: factorsOfNumber=: monad define Y=. y"_ /:~ ~. ( , Y%]) ( #~ 0=]|Y) 1+i.>.%:y ) factorsOfNumber 40 1 2 4 5 8 10 20 40 Another approach: odometer =: #: i.@(*/) factors=: (*/@:^"1 odometer@:>:)/@q:~&__ See http://www.jsoftware.com/jwiki/Essays/Odometer ## Java {{works with|Java|5+}} factors(long n) { TreeSet<Long> factors = new TreeSet<Long>(); factors.add(n); factors.add(1L); for(long test = n - 1; test >= Math.sqrt(n); test--) if(n % test == 0) { factors.add(test); factors.add(n / test); } return factors; } ## JavaScript ### Imperative function factors(num) { var n_factors = [], i; for (i = 1; i <= Math.floor(Math.sqrt(num)); i += 1) if (num % i === 0) { n_factors.push(i); if (num / i !== i) n_factors.push(num / i); } n_factors.sort(function(a, b){return a - b;}); // numeric sort return n_factors; } factors(45); // [1,3,5,9,15,45] factors(53); // [1,53] factors(64); // [1,2,4,8,16,32,64] ### Functional ### =ES5= Translating the naive list comprehension example from Haskell, using a list monad for the comprehension // Monadic bind (chain) for lists function chain(xs, f) { return [].concat.apply([], xs.map(f)); } // [m..n] function range(m, n) { return Array.apply(null, Array(n - m + 1)).map(function (x, i) { return m + i; }); } function factors_naive(n) { return chain( range(1, n), function (x) { // monadic chain/bind return n % x ? [] : [x]; // monadic fail or inject/return }); } factors_naive(6) Output: [1, 2, 3, 6] Translating the Haskell (lows and highs) example console.log( (function (lstTest) { // INTEGER FACTORS function integerFactors(n) { var rRoot = Math.sqrt(n), intRoot = Math.floor(rRoot), lows = range(1, intRoot).filter(function (x) { return (n % x) === 0; }); // for perfect squares, we can drop the head of the 'highs' list return lows.concat(lows.map(function (x) { return n / x; }).reverse().slice((rRoot === intRoot) | 0)); } // [m .. n] function range(m, n) { return Array.apply(null, Array(n - m + 1)).map(function (x, i) { return m + i; }); } /*************************** TESTING *****************************/ // TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS function alignedTable(lstRows, lngPad, fnAligned) { var lstColWidths = range(0, lstRows.reduce(function (a, x) { return x.length > a ? x.length : a; }, 0) - 1).map(function (iCol) { return lstRows.reduce(function (a, lst) { var w = lst[iCol] ? lst[iCol].toString().length : 0; return (w > a) ? w : a; }, 0); }); return lstRows.map(function (lstRow) { return lstRow.map(function (v, i) { return fnAligned(v, lstColWidths[i] + lngPad); }).join('') }).join('\n'); } function alignRight(n, lngWidth) { var s = n.toString(); return Array(lngWidth - s.length + 1).join(' ') + s; } // TEST return '\nintegerFactors(n)\n\n' + alignedTable( lstTest.map(integerFactors).map(function (x, i) { return [lstTest[i], '-->'].concat(x); }), 2, alignRight ) + '\n'; })([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767]) ); Output: integerFactors(n) 25 --> 1 5 25 45 --> 1 3 5 9 15 45 53 --> 1 53 64 --> 1 2 4 8 16 32 64 100 --> 1 2 4 5 10 20 25 50 100 102 --> 1 2 3 6 17 34 51 102 120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 12345 --> 1 3 5 15 823 2469 4115 12345 32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766 32767 --> 1 7 31 151 217 1057 4681 32767 ### =ES6= (function (lstTest) { 'use strict'; // INTEGER FACTORS // integerFactors :: Int -> [Int] let integerFactors = (n) => { let rRoot = Math.sqrt(n), intRoot = Math.floor(rRoot), lows = range(1, intRoot) .filter(x => (n % x) === 0); // for perfect squares, we can drop // the head of the 'highs' list return lows.concat(lows .map(x => n / x) .reverse() .slice((rRoot === intRoot) | 0) ); }, // range :: Int -> Int -> [Int] range = (m, n) => Array.from({ length: (n - m) + 1 }, (_, i) => m + i); /*************************** TESTING *****************************/ // TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS let alignedTable = (lstRows, lngPad, fnAligned) => { var lstColWidths = range( 0, lstRows .reduce( (a, x) => (x.length > a ? x.length : a), 0 ) - 1 ) .map((iCol) => lstRows .reduce((a, lst) => { let w = lst[iCol] ? lst[iCol].toString() .length : 0; return (w > a) ? w : a; }, 0)); return lstRows.map((lstRow) => lstRow.map((v, i) => fnAligned( v, lstColWidths[i] + lngPad )) .join('') ) .join('\n'); }, alignRight = (n, lngWidth) => { let s = n.toString(); return Array(lngWidth - s.length + 1) .join(' ') + s; }; // TEST return '\nintegerFactors(n)\n\n' + alignedTable(lstTest .map(integerFactors) .map( (x, i) => [lstTest[i], '-->'].concat(x) ), 2, alignRight ) + '\n'; })([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767]); {{Out}} integerFactors(n) 25 --> 1 5 25 45 --> 1 3 5 9 15 45 53 --> 1 53 64 --> 1 2 4 8 16 32 64 100 --> 1 2 4 5 10 20 25 50 100 102 --> 1 2 3 6 17 34 51 102 120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 12345 --> 1 3 5 15 823 2469 4115 12345 32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766 32767 --> 1 7 31 151 217 1057 4681 32767 ## jq {{Works with|jq|1.4}} # This implementation uses "sort" for tidiness def factors: . asnum
| reduce range(1; 1 + sqrt|floor) as $i ([]; if ($num % $i) == 0 then ($num / $i) as$r
| if $i ==$r then . + [$i] else . + [$i, $r] end else . end ) | sort; def task: (45, 53, 64) | "\(.): \(factors)" ; task {{Out}}$ jq -n -M -r -c -f factors.jq 45: [1,3,5,9,15,45] 53: [1,53] 64: [1,2,4,8,16,32,64]

## Julia

using Primes

function factors(n)
f = [one(n)]
for (p,e) in factor(n)
f = reduce(vcat, [f*p^j for j in 1:e], init=f)
end
return length(f) == 1 ? [one(n), n] : sort!(f)
end

const examples = [28, 45, 53, 64, 6435789435768]

for n in examples
@time println("The factors of $n are:$(factors(n))")
end

{{out}}

The factors of 28 are: [1, 2, 4, 7, 14, 28]
0.330684 seconds (784.75 k allocations: 39.104 MiB, 3.17% gc time)
The factors of 45 are: [1, 3, 5, 9, 15, 45]
0.000117 seconds (56 allocations: 2.672 KiB)
The factors of 53 are: [1, 53]
0.000102 seconds (35 allocations: 1.516 KiB)
The factors of 64 are: [1, 2, 4, 8, 16, 32, 64]
0.000093 seconds (56 allocations: 3.172 KiB)
The factors of 6435789435768 are: [1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28,
33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 191, 231, 264, 308, 382, 462, 573,
616, 764, 924, 1146, 1337, 1528, 1848, 2101, 2292, 2674, 4011, 4202, 4584, 5348,
6303, 8022, 8404, 10696, 12606, 14707, 16044, 16808, 25212, 29414, 32088, 44121,
50424, 58828, 88242, 117656, 176484, 352968, 18233351, 36466702, 54700053, 72933404,
109400106, 127633457, 145866808, 200566861, 218800212, 255266914, 382900371,
401133722, 437600424, 510533828, 601700583, 765800742, 802267444, 1021067656,
1203401166, 1403968027, 1531601484, 1604534888, 2406802332, 2807936054, 3063202968,
3482570041, 4211904081, 4813604664, 5615872108, 6965140082, 8423808162, 10447710123,
11231744216, 13930280164, 16847616324, 20895420246, 24377990287, 27860560328,
33695232648, 38308270451, 41790840492, 48755980574, 73133970861, 76616540902,
83581680984, 97511961148, 114924811353, 146267941722, 153233081804, 195023922296,
229849622706, 268157893157, 292535883444, 306466163608, 459699245412, 536315786314,
585071766888, 804473679471, 919398490824, 1072631572628, 1608947358942, 2145263145256,
3217894717884, 6435789435768]
0.000249 seconds (451 allocations: 24.813 KiB)

## K

f:{i:{y[&x=y*x div y]}[x;1+!_sqrt x];?i,x div|i}
equivalent to:
q)f:{i:{y where x=y*x div y}[x ; 1+ til floor sqrt x]; distinct i,x div reverse i}

f 120
1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120

f 1024
1 2 4 8 16 32 64 128 256 512 1024

f 600851475143
1 71 839 1471 6857 59569 104441 486847 1234169 5753023 10086647 87625999 408464633 716151937 8462696833 600851475143

#f 3491888400 / has 1920 factors
1920

/ Number of factors for 3491888400 .. 3491888409
#:'f' 3491888400+!10
1920 16 4 4 12 16 32 16 8 24

## Kotlin

fun printFactors(n: Int) {
if (n < 1) return
print("$n => ") (1..n / 2) .filter { n % it == 0 } .forEach { print("$it ") }
println(n)
}

fun main(args: Array<String>) {
val numbers = intArrayOf(11, 21, 32, 45, 67, 96)
for (number in numbers) printFactors(number)
}

{{out}}

11 => 1 11
21 => 1 3 7 21
32 => 1 2 4 8 16 32
45 => 1 3 5 9 15 45
67 => 1 67
96 => 1 2 3 4 6 8 12 16 24 32 48 96

## LFE

### Using List Comprehensions

This following function is elegant looking and concise. However, it will not handle large numbers well: it will consume a great deal of memory (on one large number, the function consumed 4.3GB of memory on my desktop machine):

(defun factors (n)
(list-comp
((<- i (when (== 0 (rem n i))) (lists:seq 1 (trunc (/ n 2)))))
i))

===Non-Stack-Consuming===

This version will not consume the stack (this function only used 18MB of memory on my machine with a ridiculously large number):

(defun factors (n)
"Tail-recursive prime factors function."
(factors n 2 '()))

(defun factors
((1 _ acc) (++ acc '(1)))
((n _ acc) (when (=< n 0))
#(error undefined))
((n k acc) (when (== 0 (rem n k)))
(factors (div n k) k (cons k acc)))
((n k acc)
(factors n (+ k 1) acc)))

{{out}}

> (factors 10677106534462215678539721403561279)
(104729 104729 104729 98731 98731 32579 29269 1)

## Liberty BASIC

num = 10677106534462215678539721403561279
maxnFactors = 1000
dim primeFactors(maxnFactors),  nPrimeFactors(maxnFactors)

print "Start finding all factors of ";num; ":"

dummy = factorize(num,2)
nFactors = showPrimeFactors(num)
dim factors(nFactors)
dummy = generateFactors(1,1)
sort factors(), 0, nFactors-1
for i=1 to nFactors
print i;"     ";factors(i-1)
next i

print "done"

wait

function factorize(iNum,offset)
factorFound=0
i = offset
do
if (iNum MOD i)=0 _
then
then
else
end if
if iNum/i<>1 then dummy = factorize(iNum/i,i)
factorFound=1
end if
i=i+1
loop while factorFound=0 and i<=sqr(iNum)
if factorFound=0 _
then
end if
end function

function showPrimeFactors(iNum)
showPrimeFactors=1
print iNum;" = ";
print primeFactors(i);"^";nPrimeFactors(i);
if i<nDifferentPrimeNumbersFound then print " * "; else print ""
showPrimeFactors = showPrimeFactors*(nPrimeFactors(i)+1)
next i
end function

function generateFactors(product,pIndex)
then
factors(iFactor) = product
iFactor=iFactor+1
else
for i=0 to nPrimeFactors(pIndex)
dummy = generateFactors(product*primeFactors(pIndex)^i,pIndex+1)
next i
end if
end function

{{out}}

Start finding all factors of 10677106534462215678539721403561279:
10677106534462215678539721403561279 = 29269^1 * 32579^1 * 98731^2 * 104729^3
1 1
2 29269
3 32579
4 98731
5 104729
6 953554751
7 2889757639
8 3065313101
9 3216557249
10 3411966091
11 9747810361
12 10339998899
13 10968163441
14 94145414120981
15 99864835517479
16 285308661456109
17 302641427774831
18 317573913751019
19 321027175754629
20 336866824130521
21 357331796744339
22 1020878431297169
23 1082897744693371
24 1148684789012489
25 9295070881578575111
26 9859755075476219149
27 10458744358910058191
28 29880090805636839461
29 31695334089430275799
30 33259198413230468851
31 33620855089606540541
32 35279725624365333809
33 37423001741237879131
34 106915577231321212201
35 113410797903992051459
36 973463478356842592799919
37 1032602289299548955255621
38 1095333837964291484285239
39 3129312029983540559911069
40 3319420643851943354153471
41 3483202590619213772296379
42 3694810384914157044482761
43 11197161487859039232598529
44 101949856624833767901342716951
45 108143405156052462534965931709
46 327729719588146219298926345301
47 364792324112959639158827476291
48 10677106534462215678539721403561279
done

### A Simpler Approach

This is a somewhat simpler approach for finding the factors of smaller numbers (less than one million).

print "ROSETTA CODE - Factors of an integer"
'A simpler approach for smaller numbers
[Start]
print
input "Enter an integer (< 1,000,000): "; n
n=abs(int(n)): if n=0 then goto [Quit]
if n>999999 then goto [Start]
FactorCount=FactorCount(n)
select case FactorCount
case 1: print "The factor of 1 is: 1"
case else
print "The "; FactorCount; " factors of "; n; " are: ";
for x=1 to FactorCount
print " "; Factor(x);
next x
if FactorCount=2 then print " (Prime)" else print
end select
goto [Start]

[Quit]
print "Program complete."
end

function FactorCount(n)
dim Factor(100)
for y=1 to n
if y>sqr(n) and FactorCount=1 then
'If no second factor is found by the square root of n, then n is prime.
FactorCount=2: Factor(FactorCount)=n: exit function
end if
if (n mod y)=0 then
FactorCount=FactorCount+1
Factor(FactorCount)=y
end if
next y
end function

{{out}}

ROSETTA CODE - Factors of an integer

Enter an integer (< 1,000,000): 1
The factor of 1 is: 1

Enter an integer (< 1,000,000): 2
The 2 factors of 2 are:  1 2 (Prime)

Enter an integer (< 1,000,000): 4
The 3 factors of 4 are:  1 2 4

Enter an integer (< 1,000,000): 6
The 4 factors of 6 are:  1 2 3 6

Enter an integer (< 1,000,000): 999999
The 64 factors of 999999 are:  1 3 7 9 11 13 21 27 33 37 39 63 77 91 99 111 117 143 189 231 259 273 297 333 351 407 429 481 693 777 819 999 1001 1221 1287 1443 2079 2331 2457 2849 3003 3367 3663 3861 4329 5291 6993 8547 9009 10101 10989 129
87 15873 25641 27027 30303 37037 47619 76923 90909 111111 142857 333333 999999

Enter an integer (< 1,000,000):
Program complete.

## Lingo

on factors(n)
res = [1]
repeat with i = 2 to n/2
if n mod i = 0 then res.add(i)
end repeat
return res
end
put factors(45)
-- [1, 3, 5, 9, 15, 45]
put factors(53)
-- [1, 53]
put factors(64)
-- [1, 2, 4, 8, 16, 32, 64]
to factors :n
output filter [equal? 0 modulo :n ?] iseq 1 :n
end

show factors 28       ; [1 2 4 7 14 28]

## Lua

function Factors( n )
local f = {}

for i = 1, n/2 do
if n % i == 0 then
f[#f+1] = i
end
end
f[#f+1] = n

return f
end

## M2000 Interpreter

\\ Factors of an integer
\\ For act as BASIC's FOR (if N<1 no loop start)
FORM 60,40
SET SWITCHES "+FOR"
MODULE LikeBasic {
10 INPUT N%
20 FOR I%=1 TO N%
30 IF N%/I%=INT(N%/I%) THEN PRINT I%,
40 NEXT I%
50 PRINT
}
CALL LikeBasic
SET SWITCHES "-FOR"
MODULE LikeM2000 {
DEF DECIMAL N%, I%
INPUT N%
IF N%<1 THEN EXIT
FOR I%=1 TO N% {
IF N% MOD I%=0 THEN PRINT I%,
}
PRINT
}
CALL LikeM2000

## Maple

numtheory:-divisors(n);

Factorize[n_Integer] := Divisors[n]

function fact(n);
f = factor(n);	% prime decomposition
K = dec2bin(0:2^length(f)-1)-'0';   % generate all possible permutations
F = ones(1,2^length(f));
for k = 1:size(K)
F(k) = prod(f(~K(k,:)));		% and compute products
end;
F = unique(F);	% eliminate duplicates
printf('There are %i factors for %i.\n',length(F),n);
disp(F);
end;

{{out}}

>> fact(12)
There are 6 factors for 12.
1    2    3    4    6   12
>> fact(28)
There are 6 factors for 28.
1    2    4    7   14   28
>> fact(64)
There are 7 factors for 64.
1    2    4    8   16   32   64
>>fact(53)
There are 2 factors for 53.
1   53

## Maxima

The builtin divisors function does this.

(%i96) divisors(100);
(%o96) {1,2,4,5,10,20,25,50,100}

Such a function could be implemented like so:

divisors2(n) := map( lambda([l], lreduce("*", l)),
apply( cartesian_product,
map( lambda([fac],
setify(makelist(fac[1]^i, i, 0, fac[2]))),
ifactors(n))));

## MAXScript

fn factors n =
(
return (for i = 1 to n+1 where mod n i == 0 collect i)
)

{{out}}

factors 3
#(1, 3)
factors 7
#(1, 7)
factors 14
#(1, 2, 7, 14)
factors 60
#(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
factors 54
#(1, 2, 3, 6, 9, 18, 27, 54)

## Mercury

Mercury is both a logic language and a functional language. As such there are two possible interfaces for calculating the factors of an integer. This code shows both styles of implementation. Note that much of the code here is ceremony put in place to have this be something which can actually compile. The actual factoring is contained in the predicate factor/2 and in the function factor/1. The function form is implemented in terms of the predicate form rather than duplicating all of the predicate code.

The predicates main/2 and factor/2 are shown with the combined type and mode statement (e.g. int::in) as is the usual case for simple predicates with only one mode. This makes the code more immediately understandable. The predicate factor/5, however, has its mode broken out onto a separate line both to show Mercury's mode statement (useful for predicates which can have varying instantiation of parameters) and to stop the code from extending too far to the right. Finally the function factor/1 has its mode statements removed (shown underneath in a comment for illustration purposes) because good coding style (and the default of the compiler!) has all parameters "in"-moded and the return value "out"-moded.

This implementation of factoring works as follows:

# If the incremental number divides evenly into the input number, both the incremental number and the quotient are added to the list of factors.

This implementation makes use of Mercury's "state variable notation" to keep a pair of variables for accumulation, thus allowing the implementation to be tail recursive. !Accumulator is syntax sugar for a pair of variables. One of them is an "in"-moded variable and the other is an "out"-moded variable. !:Accumulator is the "out" portion and !.Accumulator is the "in" portion in the ensuing code.

Using the state variable notation avoids having to keep track of strings of variables unified in the code named things like Acc0, Acc1, Acc2, Acc3, etc.

### fac.m

:- module fac.

:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.

:- implementation.
:- import_module float, int, list, math, string.

main(!IO) :-
io.command_line_arguments(Args, !IO),
list.filter_map(string.to_int, Args, CleanArgs),
list.foldl((pred(Arg::in, !.IO::di, !:IO::uo) is det :-
factor(Arg, X),
io.format("factor(%d, [", [i(Arg)], !IO),
io.write_list(X, ",", io.write_int, !IO),
io.write_string("])\n", !IO)
), CleanArgs, !IO).

:- pred factor(int::in, list(int)::out) is det.
factor(N, Factors) :-
Limit = float.truncate_to_int(math.sqrt(float(N))),
factor(N, 2, Limit, [], Unsorted),
list.sort_and_remove_dups([1, N | Unsorted], Factors).

:- pred factor(int, int, int, list(int), list(int)).
:- mode factor(in,  in,  in,  in,        out) is det.
factor(N, X, Limit, !Accumulator) :-
( if X  > Limit
then true
else ( if 0 = N mod X
then !:Accumulator = [X, N / X | !.Accumulator]
else true ),
factor(N, X + 1, Limit, !Accumulator) ).

:- func factor(int) = list(int).
%:- mode factor(in) = out is det.
factor(N) = Factors :- factor(N, Factors).

:- end_module fac.

### Use and output

Use of the code looks like this:

<nowiki>$mmc fac.m && ./fac 100 999 12345678 booger factor(100, [1,2,4,5,10,20,25,50,100]) factor(999, [1,3,9,27,37,111,333,999]) factor(12345678, [1,2,3,6,9,18,47,94,141,282,423,846,14593,29186,43779,87558,131337,262674,685871,1371742,2057613,4115226,6172839,12345678])</nowiki> =={{header|МК-61/52}}== П9 1 П6 КИП6 ИП9 ИП6 / П8 ^ [x] x#0 21 - x=0 03 ИП6 С/П ИП8 П9 БП 04 1 С/П БП 21 ## MUMPS factors(num) New fctr,list,sep,sqrt If num<1 Quit "Too small a number" If num["." Quit "Not an integer" Set sqrt=num**0.5\1 For fctr=1:1:sqrt Set:num/fctr'["." list(fctr)=1,list(num/fctr)=1 Set (list,fctr)="",sep="[" For Set fctr=$Order(list(fctr)) Quit:fctr=""  Set list=list_sep_fctr,sep=","
Quit list_"]"

w $$factors(45) ; [1,3,5,9,15,45] w$$factors(53) ; [1,53]
w factors(64) ; [1,2,4,8,16,32,64]

## NetRexx

{{trans|REXX}}

/* NetRexx ***********************************************************
* 21.04.2013 Walter Pachl
* 21.04.2013 add method main to accept argument(s)
*********************************************************************/
options replace format comments java crossref symbols nobinary
class divl
method main(argwords=String[]) static
arg=Rexx(argwords)
Parse arg a b
Say a b
If a='' Then Do
help='java divl low [high] shows'
help=help||' divisors of all numbers between low and high'
Say help
Return
End
If b='' Then b=a
loop x=a To b
say x '->' divs(x)
End

method divs(x) public static returns Rexx
if x==1 then return 1               /*handle special case of 1     */
lo=1
hi=x
odd=x//2                            /* 1 if x is odd               */
loop j=2+odd By 1+odd While j*j<x   /*divide by numbers<sqrt(x)    */
if x//j==0 then Do                /*Divisible?  Add two divisors:*/
lo=lo j                         /* list low divisors           */
hi=x%j hi                       /* list high divisors          */
End
End
If j*j=x Then                       /*for a square number as input */
lo=lo j                           /* add its square root         */
return lo hi                        /* return both lists           */

{{out}}

java divl 1 10
1 -> 1
2 -> 1 2
3 -> 1 3
4 -> 1 2 4
5 -> 1 5
6 -> 1 2 3 6
7 -> 1 7
8 -> 1 2 4 8
9 -> 1 3 9
10 -> 1 2 5 10

## Nim

import intsets, math, algorithm

proc factors(n): seq[int] =
var fs = initIntSet()
for x in 1 .. int(sqrt(float(n))):
if n mod x == 0:
fs.incl(x)
fs.incl(n div x)

result = @[]
for x in fs:
sort(result, system.cmp[int])

echo factors(45)

## Niue

[ 'n ; [ negative-or-zero [ , ] if
[ n not-factor [ , ] when ] else ] n times n ] 'factors ;

[ dup 0 <= ] 'negative-or-zero ;
[ swap dup rot swap mod 0 = not ] 'not-factor ;

( tests )
100 factors .s .clr ( => 1 2 4 5 10 20 25 50 100 ) newline
53 factors .s .clr ( => 1 53 ) newline
64 factors .s .clr ( => 1 2 4 8 16 32 64 ) newline
12 factors .s .clr ( => 1 2 3 4 6 12 )

MODULE Factors;
IMPORT Out,SYSTEM;
TYPE
LIPool = POINTER TO ARRAY OF LONGINT;
LIVector= POINTER TO LIVectorDesc;
LIVectorDesc = RECORD
cap: INTEGER;
len: INTEGER;
LIPool: LIPool;
END;

PROCEDURE New(cap: INTEGER): LIVector;
VAR
v: LIVector;
BEGIN
NEW(v);
v.cap := cap;
v.len := 0;
NEW(v.LIPool,cap);
RETURN v
END New;

VAR
newLIPool: LIPool;
BEGIN
IF v.len = LEN(v.LIPool^) THEN
(* run out of space *)
v.cap := v.cap + (v.cap DIV 2);
NEW(newLIPool,v.cap);
v.LIPool := newLIPool
END;
v.LIPool[v.len] := x;
INC(v.len)

PROCEDURE (v: LIVector) At(idx: INTEGER): LONGINT;
BEGIN
RETURN v.LIPool[idx];
END At;

PROCEDURE Factors(n:LONGINT): LIVector;
VAR
j: LONGINT;
v: LIVector;
BEGIN
v := New(16);
FOR j := 1 TO n DO
IF (n MOD j) = 0 THEN v.Add(j) END;
END;
RETURN v
END Factors;

VAR
v: LIVector;
j: INTEGER;
BEGIN
v := Factors(123);
FOR j := 0 TO v.len - 1 DO
Out.LongInt(v.At(j),4);Out.Ln
END;
Out.Int(v.len,6);Out.String(" factors");Out.Ln
END Factors.

{{out}}

1
3
41
123
4 factors

## Objeck

use IO;
use Structure;

bundle Default {
class Basic {
function : native : GenerateFactors(n : Int)  ~ IntVector {
factors := IntVector->New();

for(i := 2; i * i <= n; i += 1;) {
if(n % i = 0) {
if(i * i <> n) {
};
};
};
factors->Sort();

return factors;
}

function : Main(args : String[]) ~ Nil {
numbers := [3135, 45, 60, 81];
for(i := 0; i < numbers->Size(); i += 1;) {
factors := GenerateFactors(numbers[i]);

Console->GetInstance()->Print("Factors of ")->Print(numbers[i])->PrintLine(" are:");
each(i : factors) {
Console->GetInstance()->Print(factors->Get(i))->Print(", ");
};
"\n\n"->Print();
};
}
}
}

## OCaml

let rec range = function 0 -> [] | n -> range(n-1) @ [n]

let factors n =
List.filter (fun v -> (n mod v) = 0) (range n)

## Oforth

Integer method: factors  self seq filter(#[ self isMultiple ]) ;

120 factors println

{{out}}

[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]

## Oz

declare
fun {Factors N}
Sqr = {Float.toInt {Sqrt {Int.toFloat N}}}

Fs = for X in 1..Sqr append:App do
if N mod X == 0 then
CoFactor = N div X
in
if CoFactor == X then %% avoid duplicate factor
{App [X]}          %% when N is a square number
else
{App [X CoFactor]}
end
end
end
in
{Sort Fs Value.'<'}
end
in
{Show {Factors 53}}

divisors(n)

## Panda

Panda has a factor function already, it's defined as:

fun factor(n) type integer->integer
f where n.mod(1..n=>f)==0

45.factor

## Pascal

{{trans|Fortran}} {{works with|Free Pascal|2.6.2}}

program Factors;
var
i, number: integer;
begin
write('Enter a number between 1 and 2147483647: ');

for i := 1 to round(sqrt(number)) - 1 do
if number mod i = 0 then
write (i, ' ',  number div i, ' ');

// Check to see if number is a square
i := round(sqrt(number));
if i*i = number then
write(i)
else if number mod i = 0 then
write(i, number/i);
writeln;
end.

{{out}}

Enter a number between 1 and 2147483647: 49
1 49 7

Enter a number between 1 and 2147483647: 353435
1 25755 3 8585 5 5151 15 1717 17 1515 51 505 85 303 101 255

### small improvement

the factors are in ascending order. {{works with|Free Pascal}}

program factors;
{Looking for extreme composite numbers:
http://wwwhomes.uni-bielefeld.de/achim/highly.txt}

const
MAXFACTORCNT = 1920; //number := 3491888400;

var
FaktorList : array[0..MAXFACTORCNT] of LongWord;
i, number,quot,cnt: LongWord;
begin
writeln('Enter a number between 1 and 4294967295: ');
write('3491888400 is a nice choice ');

cnt := 0;
i := 1;
repeat
quot := number div i;
if quot *i-number = 0 then
begin
FaktorList[cnt] := i;
FaktorList[MAXFACTORCNT-cnt] := quot;
inc(cnt);
end;
inc(i);
until i> quot;
writeln(number,' has ',2*cnt,' factors');
dec(cnt);
For i := 0 to cnt do
write(FaktorList[i],' ,');
For i := cnt downto 1 do
write(FaktorList[MAXFACTORCNT-i],' ,');
{ the last without ','}
writeln(FaktorList[MAXFACTORCNT]);
end.

{{out}}

Enter a number between 1 and 4294967295:
3491888400 is a nice choice 120
120 has 16 factors
1 ,2 ,3 ,4 ,5 ,6 ,8 ,10 ,12 ,15 ,20 ,24 ,30 ,40 ,60 ,120

## Perl

sub factors
{
my($n) = @_; return grep {$n % $_ == 0 }(1 ..$n);
}
print join ' ',factors(64), "\n";

Or more intelligently:

sub factors {
my $n = shift;$n = -$n if$n < 0;
my @divisors;
for (1 .. int(sqrt($n))) { # faster and less memory than map/grep push @divisors,$_ unless $n %$_;
}
# Return divisors including top half, without duplicating a square

## Phix

There is a builtin factors(n), which takes an optional second parameter to include 1 and n, so eg ?factors(12345,1) displays {{out}}

{1,3,5,15,823,2469,4115,12345}

You can find the implementation of factors() and prime_factors() in builtins\pfactors.e

## PHP

function GetFactors($n){$factors = array(1, $n); for($i = 2; $i *$i <= $n;$i++){
if($n %$i == 0){
$factors[] =$i;
if($i *$i != $n)$factors[] = $n/$i;
}
}
sort($factors); return$factors;
}

## PicoLisp

(de factors (N)
(filter
'((D) (=0 (% N D)))
(range 1 N) ) )

## PILOT

T  :Enter a number.
A  :#n
C  :factor = 1
T  :The factors of #n are:
*Loop
C  :remainder = n % factor
T ( remainder = 0 )  :#factor
J ( factor = n )     :*Finished
C  :factor = factor + 1
J  :*Loop
*Finished
END:

## PL/I

do i = 1 to n;
if mod(n, i) = 0 then put skip list (i);
end;

## PowerShell

### Straightforward but slow

function Get-Factor ($a) { 1..$a | Where-Object { $a %$_ -eq 0 }
}

This one uses a range of integers up to the target number and just filters it using the Where-Object cmdlet. It's very slow though, so it is not very usable for larger numbers.

### A little more clever

function Get-Factor ($a) { 1..[Math]::Sqrt($a) 
| Where-Object { $a %$_ -eq 0 }
| ForEach-Object { $_;$a / $_ }  | Sort-Object -Unique } Here the range of integers is only taken up to the square root of the number, the same filtering applies. Afterwards the corresponding larger factors are calculated and sent down the pipeline along with the small ones found earlier. ## ProDOS Uses the math module: editvar /newvar /value=a /userinput=1 /title=Enter an integer: do /delimspaces %% -a- >b printline Factors of -a-: -b- ## Prolog '''Simple Brute Force Implementation''' brute_force_factors( N , Fs ) :- integer(N) , N > 0 , setof( F , ( between(1,N,F) , N mod F =:= 0 ) , Fs ) . '''A Slightly Smarter Implementation''' smart_factors(N,Fs) :- integer(N) , N > 0 , setof( F , factor(N,F) , Fs ) . factor(N,F) :- L is floor(sqrt(N)) , between(1,L,X) , 0 =:= N mod X , ( F = X ; F is N // X ) . Not every Prolog has between/3: you might need this: between(X,Y,Z) :- integer(X) , integer(Y) , X =< Z , between1(X,Y,Z) . between1(X,Y,X) :- X =< Y . between1(X,Y,Z) :- X < Y , X1 is X+1 , between1(X1,Y,Z) . {{out}} ?- N=36 ,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ). N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] ; N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] . ?- N=53,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ). N = 53, Factors = [1, 53] ; N = 53, Factors = [1, 53] . ?- N=100,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] ; N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] . ?- N=144,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] ; N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] . ?- N=32765,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32765, Factors = [1, 5, 6553, 32765] ; N = 32765, Factors = [1, 5, 6553, 32765] . ?- N=32766,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] ; N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] . 38 ?- N=32767,( brute_force_factors(N,Factors);smart_factors(N,Factors) ). N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] ; N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] . ## PureBasic Procedure PrintFactors(n) Protected i, lim=Round(sqr(n),#PB_Round_Up) NewList F.i() For i=1 To lim If n%i=0 AddElement(F()): F()=i AddElement(F()): F()=n/i EndIf Next ;- Present the result SortList(F(),#PB_Sort_Ascending) ForEach F() Print(str(F())+" ") Next EndProcedure If OpenConsole() Print("Enter integer to factorize: ") PrintFactors(Val(Input())) Print(#CRLF$+#CRLF$+"Press ENTER to quit."): Input() EndIf {{out}} Enter integer to factorize: 96 1 2 3 4 6 8 12 16 24 32 48 96 ## Python Naive and slow but simplest (check all numbers from 1 to n): def factors(n): return [i for i in range(1, n + 1) if not n%i] Slightly better (realize that there are no factors between n/2 and n): def factors(n): return [i for i in range(1, n//2 + 1) if not n%i] + [n] >>> factors(45) [1, 3, 5, 9, 15, 45] Much better (realize that factors come in pairs, the smaller of which is no bigger than sqrt(n)): from math import sqrt >>> def factor(n): factors = set() for x in range(1, int(sqrt(n)) + 1): if n % x == 0: factors.add(x) factors.add(n//x) return sorted(factors) >>> for i in (45, 53, 64): print( "%i: factors: %s" % (i, factor(i)) ) 45: factors: [1, 3, 5, 9, 15, 45] 53: factors: [1, 53] 64: factors: [1, 2, 4, 8, 16, 32, 64] More efficient when factoring many numbers: from itertools import chain, cycle, accumulate # last of which is Python 3 only def factors(n): def prime_powers(n): # c goes through 2, 3, 5, then the infinite (6n+1, 6n+5) series for c in accumulate(chain([2, 1, 2], cycle([2,4]))): if c*c > n: break if n%c: continue d,p = (), c while not n%c: n,p,d = n//c, p*c, d + (p,) yield(d) if n > 1: yield((n,)) r = [1] for e in prime_powers(n): r += [a*b for a in r for b in e] return r ## R factors <- function(n) { if(length(n) > 1) { lapply(as.list(n), factors) } else { one.to.n <- seq_len(n) one.to.n[(n %% one.to.n) == 0] } } factors(60) 1 2 3 4 5 6 10 12 15 20 30 60 factors(c(45, 53, 64)) [[1]] [1] 1 3 5 9 15 45 [[2]] [1] 1 53 [[3]] [1] 1 2 4 8 16 32 64 ## Racket #lang racket ;; a naive version (define (naive-factors n) (for/list ([i (in-range 1 (add1 n))] #:when (zero? (modulo n i))) i)) (naive-factors 120) ; -> '(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120) ;; much better: use factorize' to get prime factors and construct the ;; list of results from that (require math) (define (factors n) (sort (for/fold ([l '(1)]) ([p (factorize n)]) (append (for*/list ([e (in-range 1 (add1 (cadr p)))] [x l]) (* x (expt (car p) e))) l)) <)) (naive-factors 120) ; -> same ;; to see how fast it is: (define huge 1200034005600070000008900000000000000000) (time (length (factors huge))) ;; I get 42ms for getting a list of 7776 numbers ;; but actually the math library comes with a divisors' function that ;; does the same, except even faster (divisors 120) ; -> same (time (length (divisors huge))) ;; And this one clocks at 17ms ## REALbasic Function factors(num As UInt64) As UInt64() 'This function accepts an unsigned 64 bit integer as input and returns an array of unsigned 64 bit integers Dim result() As UInt64 Dim iFactor As UInt64 = 1 While iFactor <= num/2 'Since a factor will never be larger than half of the number If num Mod iFactor = 0 Then result.Append(iFactor) End If iFactor = iFactor + 1 Wend result.Append(num) 'Since a given number is always a factor of itself Return result End Function ## REXX ### optimized version This REXX version has no effective limits on the number of decimal digits in the number to be factored [by adjusting the number of digits (precision)]. This REXX version also supports negative integers and zero. It also indicates '''primes''' in the output listing as well as the number of factors. It also displays a final count of the number of primes found. /*REXX program displays divisors of any [negative/zero/positive] integer or a range.*/ parse arg LO HI inc . /*obtain the optional args*/ HI=word(HI LO 20, 1); LO=word(LO 1, 1); inc=word(inc 1, 1) /*define the range options*/ w=length(high)+2; numeric digits max(9, w-2);$='∞'   /*decimal digits for  //  */
@.=left('',7);  @.1="{unity}"; @.2='[prime]'; @.$=" {"$'}  ' /*define some literals.   */
say center('n', w)    "#divisors"    center('divisors', 60)   /*display the  header.    */
say copies('═', w)    "═════════"    copies('═'       , 60)   /*   "     "   separator. */
p#=0                                                          /*count of prime numbers. */
do n=LO  to HI  by inc; divs=divisors(n); #=words(divs)  /*get list of divs; # divs*/
if divs==$then do; #=$ ; divs= '  (infinite)';  end   /*handle case for infinity*/
p=@.#;      if n<0  then if n\==-1  then p=@..           /*   "     "   "  negative*/
if p==@.2  then p#=p#+1                                  /*Prime? Then bump counter*/
say center(n, w)      center('['#"]", 9)       "──► "        p      ' '       divs
end   /*n*/                                 /* [↑]   process a range of integers.  */
say
say left('', 17)     p#    ' primes were found.' /*display the number of primes found.  */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
divisors: procedure; parse arg x 1 b;     a=1    /*set  X  and  B  to the 1st argument. */
if x<2  then do; x=abs(x);  if x==1  then return 1;  if x==0  then return '∞';  b=x;  end
odd=x//2                                         /* [↓]  process EVEN or ODD ints.   ___*/
do j=2+odd  by 1+odd  while j*j<x        /*divide by all the integers up to √ x */
if x//j==0  then do; a=a j; b=x%j b; end /*÷?  Add factors to  α  and  ß  lists.*/
end   /*j*/                              /* [↑]  %  ≡  integer division.     ___*/
if j*j==x  then  return  a j b                   /*Was  X  a square?   Then insert  √ x */
return  a   b                   /*return the divisors of both lists.   */

'''output''' when the input used is: -6 200

n    #divisors                           divisors
══════ ═════════ ════════════════════════════════════════════════════════════
-6      [4]    ──►            1 2 3 6
-5      [2]    ──►            1 5
-4      [3]    ──►            1 2 4
-3      [2]    ──►            1 3
-2      [2]    ──►            1 2
-1      [1]    ──►  {unity}   1
0       [∞]    ──►    {∞}       (infinite)
1       [1]    ──►  {unity}   1
2       [2]    ──►  [prime]   1 2
3       [2]    ──►  [prime]   1 3
4       [3]    ──►            1 2 4
5       [2]    ──►  [prime]   1 5
6       [4]    ──►            1 2 3 6
7       [2]    ──►  [prime]   1 7
8       [4]    ──►            1 2 4 8
9       [3]    ──►            1 3 9
10      [4]    ──►            1 2 5 10
11      [2]    ──►  [prime]   1 11
12      [6]    ──►            1 2 3 4 6 12
13      [2]    ──►  [prime]   1 13
14      [4]    ──►            1 2 7 14
15      [4]    ──►            1 3 5 15
16      [5]    ──►            1 2 4 8 16
17      [2]    ──►  [prime]   1 17
18      [6]    ──►            1 2 3 6 9 18
19      [2]    ──►  [prime]   1 19
20      [6]    ──►            1 2 4 5 10 20
21      [4]    ──►            1 3 7 21
22      [4]    ──►            1 2 11 22
23      [2]    ──►  [prime]   1 23
24      [8]    ──►            1 2 3 4 6 8 12 24
25      [3]    ──►            1 5 25
26      [4]    ──►            1 2 13 26
27      [4]    ──►            1 3 9 27
28      [6]    ──►            1 2 4 7 14 28
29      [2]    ──►  [prime]   1 29
30      [8]    ──►            1 2 3 5 6 10 15 30
31      [2]    ──►  [prime]   1 31
32      [6]    ──►            1 2 4 8 16 32
33      [4]    ──►            1 3 11 33
34      [4]    ──►            1 2 17 34
35      [4]    ──►            1 5 7 35
36      [9]    ──►            1 2 3 4 6 9 12 18 36
37      [2]    ──►  [prime]   1 37
38      [4]    ──►            1 2 19 38
39      [4]    ──►            1 3 13 39
40      [8]    ──►            1 2 4 5 8 10 20 40
41      [2]    ──►  [prime]   1 41
42      [8]    ──►            1 2 3 6 7 14 21 42
43      [2]    ──►  [prime]   1 43
44      [6]    ──►            1 2 4 11 22 44
45      [6]    ──►            1 3 5 9 15 45
46      [4]    ──►            1 2 23 46
47      [2]    ──►  [prime]   1 47
48     [10]    ──►            1 2 3 4 6 8 12 16 24 48
49      [3]    ──►            1 7 49
50      [6]    ──►            1 2 5 10 25 50
51      [4]    ──►            1 3 17 51
52      [6]    ──►            1 2 4 13 26 52
53      [2]    ──►  [prime]   1 53
54      [8]    ──►            1 2 3 6 9 18 27 54
55      [4]    ──►            1 5 11 55
56      [8]    ──►            1 2 4 7 8 14 28 56
57      [4]    ──►            1 3 19 57
58      [4]    ──►            1 2 29 58
59      [2]    ──►  [prime]   1 59
60     [12]    ──►            1 2 3 4 5 6 10 12 15 20 30 60
61      [2]    ──►  [prime]   1 61
62      [4]    ──►            1 2 31 62
63      [6]    ──►            1 3 7 9 21 63
64      [7]    ──►            1 2 4 8 16 32 64
65      [4]    ──►            1 5 13 65
66      [8]    ──►            1 2 3 6 11 22 33 66
67      [2]    ──►  [prime]   1 67
68      [6]    ──►            1 2 4 17 34 68
69      [4]    ──►            1 3 23 69
70      [8]    ──►            1 2 5 7 10 14 35 70
71      [2]    ──►  [prime]   1 71
72     [12]    ──►            1 2 3 4 6 8 9 12 18 24 36 72
73      [2]    ──►  [prime]   1 73
74      [4]    ──►            1 2 37 74
75      [6]    ──►            1 3 5 15 25 75
76      [6]    ──►            1 2 4 19 38 76
77      [4]    ──►            1 7 11 77
78      [8]    ──►            1 2 3 6 13 26 39 78
79      [2]    ──►  [prime]   1 79
80     [10]    ──►            1 2 4 5 8 10 16 20 40 80
81      [5]    ──►            1 3 9 27 81
82      [4]    ──►            1 2 41 82
83      [2]    ──►  [prime]   1 83
84     [12]    ──►            1 2 3 4 6 7 12 14 21 28 42 84
85      [4]    ──►            1 5 17 85
86      [4]    ──►            1 2 43 86
87      [4]    ──►            1 3 29 87
88      [8]    ──►            1 2 4 8 11 22 44 88
89      [2]    ──►  [prime]   1 89
90     [12]    ──►            1 2 3 5 6 9 10 15 18 30 45 90
91      [4]    ──►            1 7 13 91
92      [6]    ──►            1 2 4 23 46 92
93      [4]    ──►            1 3 31 93
94      [4]    ──►            1 2 47 94
95      [4]    ──►            1 5 19 95
96     [12]    ──►            1 2 3 4 6 8 12 16 24 32 48 96
97      [2]    ──►  [prime]   1 97
98      [6]    ──►            1 2 7 14 49 98
99      [6]    ──►            1 3 9 11 33 99
100      [9]    ──►            1 2 4 5 10 20 25 50 100
101      [2]    ──►  [prime]   1 101
102      [8]    ──►            1 2 3 6 17 34 51 102
103      [2]    ──►  [prime]   1 103
104      [8]    ──►            1 2 4 8 13 26 52 104
105      [8]    ──►            1 3 5 7 15 21 35 105
106      [4]    ──►            1 2 53 106
107      [2]    ──►  [prime]   1 107
108     [12]    ──►            1 2 3 4 6 9 12 18 27 36 54 108
109      [2]    ──►  [prime]   1 109
110      [8]    ──►            1 2 5 10 11 22 55 110
111      [4]    ──►            1 3 37 111
112     [10]    ──►            1 2 4 7 8 14 16 28 56 112
113      [2]    ──►  [prime]   1 113
114      [8]    ──►            1 2 3 6 19 38 57 114
115      [4]    ──►            1 5 23 115
116      [6]    ──►            1 2 4 29 58 116
117      [6]    ──►            1 3 9 13 39 117
118      [4]    ──►            1 2 59 118
119      [4]    ──►            1 7 17 119
120     [16]    ──►            1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
121      [3]    ──►            1 11 121
122      [4]    ──►            1 2 61 122
123      [4]    ──►            1 3 41 123
124      [6]    ──►            1 2 4 31 62 124
125      [4]    ──►            1 5 25 125
126     [12]    ──►            1 2 3 6 7 9 14 18 21 42 63 126
127      [2]    ──►  [prime]   1 127
128      [8]    ──►            1 2 4 8 16 32 64 128
129      [4]    ──►            1 3 43 129
130      [8]    ──►            1 2 5 10 13 26 65 130
131      [2]    ──►  [prime]   1 131
132     [12]    ──►            1 2 3 4 6 11 12 22 33 44 66 132
133      [4]    ──►            1 7 19 133
134      [4]    ──►            1 2 67 134
135      [8]    ──►            1 3 5 9 15 27 45 135
136      [8]    ──►            1 2 4 8 17 34 68 136
137      [2]    ──►  [prime]   1 137
138      [8]    ──►            1 2 3 6 23 46 69 138
139      [2]    ──►  [prime]   1 139
140     [12]    ──►            1 2 4 5 7 10 14 20 28 35 70 140
141      [4]    ──►            1 3 47 141
142      [4]    ──►            1 2 71 142
143      [4]    ──►            1 11 13 143
144     [15]    ──►            1 2 3 4 6 8 9 12 16 18 24 36 48 72 144
145      [4]    ──►            1 5 29 145
146      [4]    ──►            1 2 73 146
147      [6]    ──►            1 3 7 21 49 147
148      [6]    ──►            1 2 4 37 74 148
149      [2]    ──►  [prime]   1 149
150     [12]    ──►            1 2 3 5 6 10 15 25 30 50 75 150
151      [2]    ──►  [prime]   1 151
152      [8]    ──►            1 2 4 8 19 38 76 152
153      [6]    ──►            1 3 9 17 51 153
154      [8]    ──►            1 2 7 11 14 22 77 154
155      [4]    ──►            1 5 31 155
156     [12]    ──►            1 2 3 4 6 12 13 26 39 52 78 156
157      [2]    ──►  [prime]   1 157
158      [4]    ──►            1 2 79 158
159      [4]    ──►            1 3 53 159
160     [12]    ──►            1 2 4 5 8 10 16 20 32 40 80 160
161      [4]    ──►            1 7 23 161
162     [10]    ──►            1 2 3 6 9 18 27 54 81 162
163      [2]    ──►  [prime]   1 163
164      [6]    ──►            1 2 4 41 82 164
165      [8]    ──►            1 3 5 11 15 33 55 165
166      [4]    ──►            1 2 83 166
167      [2]    ──►  [prime]   1 167
168     [16]    ──►            1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168
169      [3]    ──►            1 13 169
170      [8]    ──►            1 2 5 10 17 34 85 170
171      [6]    ──►            1 3 9 19 57 171
172      [6]    ──►            1 2 4 43 86 172
173      [2]    ──►  [prime]   1 173
174      [8]    ──►            1 2 3 6 29 58 87 174
175      [6]    ──►            1 5 7 25 35 175
176     [10]    ──►            1 2 4 8 11 16 22 44 88 176
177      [4]    ──►            1 3 59 177
178      [4]    ──►            1 2 89 178
179      [2]    ──►  [prime]   1 179
180     [18]    ──►            1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180
181      [2]    ──►  [prime]   1 181
182      [8]    ──►            1 2 7 13 14 26 91 182
183      [4]    ──►            1 3 61 183
184      [8]    ──►            1 2 4 8 23 46 92 184
185      [4]    ──►            1 5 37 185
186      [8]    ──►            1 2 3 6 31 62 93 186
187      [4]    ──►            1 11 17 187
188      [6]    ──►            1 2 4 47 94 188
189      [8]    ──►            1 3 7 9 21 27 63 189
190      [8]    ──►            1 2 5 10 19 38 95 190
191      [2]    ──►  [prime]   1 191
192     [14]    ──►            1 2 3 4 6 8 12 16 24 32 48 64 96 192
193      [2]    ──►  [prime]   1 193
194      [4]    ──►            1 2 97 194
195      [8]    ──►            1 3 5 13 15 39 65 195
196      [9]    ──►            1 2 4 7 14 28 49 98 196
197      [2]    ──►  [prime]   1 197
198     [12]    ──►            1 2 3 6 9 11 18 22 33 66 99 198
199      [2]    ──►  [prime]   1 199
200     [12]    ──►            1 2 4 5 8 10 20 25 40 50 100 200

Primes that were found:  46



### Alternate Version

REXX
/* REXX ***************************************************************
* Program to calculate and show divisors of positive integer(s).
* 03.08.2012 Walter Pachl  simplified the above somewhat
*            in particular I see no benefit from divAdd procedure
* 04.08.2012 the reference to 'above' is no longer valid since that
*            was meanwhile changed for the better.
* 04.08.2012 took over some improvements from new above
**********************************************************************/
Parse arg low high .
Select
When low=''  Then Parse Value '1 200' with low high
When high='' Then high=low
Otherwise Nop
End
do j=low to high
say '   n = ' right(j,6) "   divisors = " divs(j)
end
exit

divs: procedure; parse arg x
if x==1 then return 1               /*handle special case of 1     */
Parse Value '1' x With lo hi        /*initialize lists: lo=1 hi=x  */
odd=x//2                            /* 1 if x is odd               */
Do j=2+odd By 1+odd While j*j\sqrt{n}, we can write

ruby
class Integer
def factors
1.upto(Math.sqrt(self)).select {|i| (self % i).zero?}.inject([]) do |f, i|
f << self/i unless i == self/i
f << i
end.sort
end
end
[45, 53, 64].each {|n| puts "#{n} : #{n.factors}"}


{{out}}

txt

45 : [1, 3, 5, 9, 15, 45]
53 : [1, 53]
64 : [1, 2, 4, 8, 16, 32, 64]


### Using the prime library

ruby

require 'prime'

def factors m
return [1] if 1==m
primes, powers = Prime.prime_division(m).transpose
ranges = powers.map{|n| (0..n).to_a}
ranges[0].product( *ranges[1..-1] ).
map{|es| primes.zip(es).map{|p,e| p**e}.reduce :*}.
sort
end

[1, 7, 45, 100].each{|n| p factors n}



Output:

txt

[1]
[1, 7]
[1, 3, 5, 9, 15, 45]
[1, 2, 4, 5, 10, 20, 25, 50, 100]



## Run BASIC

runbasic
PRINT "Factors of 45 are ";factorlist$(45) PRINT "Factors of 12345 are "; factorlist$(12345)
END

function factorlist$(f) DIM L(100) FOR i = 1 TO SQR(f) IF (f MOD i) = 0 THEN L(c) = i c = c + 1 IF (f <> i^2) THEN L(c) = (f / i) c = c + 1 END IF END IF NEXT i s = 1 while s = 1 s = 0 for i = 0 to c-1 if L(i) > L(i+1) and L(i+1) <> 0 then t = L(i) L(i) = L(i+1) L(i+1) = t s = 1 end if next i wend FOR i = 0 TO c-1 factorlist$ = factorlist$+ STR$(L(i)) + ", "
NEXT
end function


{{out}}

txt
Factors of 45 are 1, 3, 5, 9, 15, 45,
Factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345,


## Rust

rust
fn main() {
assert_eq!(vec![1, 2, 4, 5, 10, 10, 20, 25, 50, 100], factor(100)); // asserts that two expressions are equal to each other
assert_eq!(vec![1, 101], factor(101));

}

fn factor(num: i32) -> Vec {
let mut factors: Vec = Vec::new(); // creates a new vector for the factors of the number

for i in 1..((num as f32).sqrt() as i32 + 1) {
if num % i == 0 {
factors.push(i); // pushes smallest factor to factors
factors.push(num/i); // pushes largest factor to factors
}
}
factors.sort(); // sorts the factors into numerical order for viewing purposes
factors // returns the factors
}


Alternative functional version:

rust

fn factor(n: i32) -> Vec {
(1..=n).filter(|i| n % i == 0).collect()
}



## Sather

{{trans|C++}}

sather
class MAIN is

factors(n :INT):ARRAY{INT} is
f:ARRAY{INT};
f := #;
f := f.append(|1|);
f := f.append(|n|);
loop i ::= 2.upto!( n.flt.sqrt.int );
if n%i = 0 then
f := f.append(|i|);
if (i*i) /= n then f := f.append(|n / i|); end;
end;
end;
f.sort;
return f;
end;

main is
a :ARRAY{INT} := |3135, 45, 64, 53, 45, 81|;
loop l ::= a.elt!;
#OUT + "factors of " + l + ": ";
r ::= factors(l);
loop ri ::= r.elt!;
#OUT + ri + " ";
end;
#OUT + "\n";
end;
end;
end;


## Scala

Scala

Brute force approach:

def factors(num: Int) = {
(1 to num).filter { divisor =>
num % divisor == 0
}
}
Since factors can't be higher than sqrt(num), the code above can be edited as follows
def factors(num: Int) = {
(1 to sqrt(num)).filter { divisor =>
num % divisor == 0
}
}



## Scheme

This implementation uses a naive trial division algorithm.

scheme
(define (factors n)
(define (*factors d)
(cond ((> d n) (list))
((= (modulo n d) 0) (cons d (*factors (+ d 1))))
(else (*factors (+ d 1)))))
(*factors 1))

(display (factors 1111111))
(newline)


{{out}}

txt

(1 239 4649 1111111)



## Seed7

seed7
$include "seed7_05.s7i"; const proc: writeFactors (in integer: number) is func local var integer: testNum is 0; begin write("Factors of " <& number <& ": "); for testNum range 1 to sqrt(number) do if number rem testNum = 0 then if testNum <> 1 then write(", "); end if; write(testNum); if testNum <> number div testNum then write(", " <& number div testNum); end if; end if; end for; writeln; end func; const proc: main is func local const array integer: numsToFactor is [] (45, 53, 64); var integer: number is 0; begin for number range numsToFactor do writeFactors(number); end for; end func;  {{out}} txt Factors of 45: 1, 45, 3, 15, 5, 9 Factors of 53: 1, 53 Factors of 64: 1, 64, 2, 32, 4, 16, 8  ## SequenceL '''Brute Force Method''' A simple brute force method using an indexed partial function as a filter. sequencel Factors(num(0))[i] := i when num mod i = 0 foreach i within 1 ... num;  '''Slightly More Efficient Method''' A slightly more efficient method, only going up to the sqrt(n). sequencel Factors(num(0)) := let factorPairs[i] := [i] when i = sqrt(num) else [i, num/i] when num mod i = 0 foreach i within 1 ... floor(sqrt(num)); in join(factorPairs);  ## Sidef ruby func factors(n) { gather { { |d| take(d, n//d) if d.divides(n) } << 1..n.isqrt }.sort.uniq } for n [53, 64, 32766] { say "factors(#{n}): #{factors(n)}" }  {{out}} txt factors(53): [1, 53] factors(64): [1, 2, 4, 8, 16, 32, 64] factors(32766): [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766]  ## Slate slate n@(Integer traits) primeFactors [ [| :result | result nextPut: 1. n primesDo: [| :prime | result nextPut: prime]] writingAs: {} ].  where primesDo: is a part of the standard numerics library: slate n@(Integer traits) primesDo: block "Decomposes the Integer into primes, applying the block to each (in increasing order)." [| div next remaining | div: 2. next: 3. remaining: n. [[(remaining \\ div) isZero] whileTrue: [block applyTo: {div}. remaining: remaining // div]. remaining = 1] whileFalse: [div: next. next: next + 2] "Just looks at the next odd integer." ].  ## Smalltalk Copied from the Python example, but code added to the Integer built in class: smalltalk>Integer> factors | a | a := OrderedCollection new. 1 to: (self / 2) do: [ :i | ((self \\ i) = 0) ifTrue: [ a add: i ] ]. a add: self. ^a  Then use as follows: smalltalk 59 factors -> an OrderedCollection(1 59) 120 factors -> an OrderedCollection(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120)  ## Standard ML Need to print the list because Standard ML truncates the display of longer returned lists. Standard ML fun printIntList ls = ( List.app (fn n => print(Int.toString n ^ " ")) ls; print "\n" ); fun factors n = let fun factors'(n, k) = if k > n then [] else if n mod k = 0 then k :: factors'(n, k+1) else factors'(n, k+1) in factors'(n,1) end;  Call: Standard ML printIntList(factors 12345) printIntList(factors 120)  {{out}} txt 1 3 5 15 823 2469 4115 12345 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60  ## Swift Simple implementation: Swift func factors(n: Int) -> [Int] { return filter(1...n) { n %$0 == 0 }
}


More efficient implementation:

Swift
import func Darwin.sqrt

func sqrt(x:Int) -> Int { return Int(sqrt(Double(x))) }

func factors(n: Int) -> [Int] {

var result = [Int]()

for factor in filter (1...sqrt(n), { n % $0 == 0 }) { result.append(factor) if n/factor != factor { result.append(n/factor) } } return sorted(result) }  Call: Swift println(factors(4)) println(factors(1)) println(factors(25)) println(factors(63)) println(factors(19)) println(factors(768))  {{out}} txt [1, 2, 4] [1] [1, 5, 25] [1, 3, 7, 9, 21, 63] [1, 19] [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768]  ## Tcl tcl proc factors {n} { set factors {} for {set i 1} {$i <= sqrt($n)} {incr i} { if {$n % $i == 0} { lappend factors$i [expr {$n /$i}]
}
}
return [lsort -unique -integer $factors] } puts [factors 64] puts [factors 45] puts [factors 53]  {{out}} txt 1 2 4 8 16 32 64 1 3 5 9 15 45 1 53  ## UNIX Shell This should work in all Bourne-compatible shells, assuming the system has both sort and at least one of bc or dc. factor() { r=echo "sqrt($1)" | bc # or echo $1 v p | dc i=1 while [$i -lt $r ]; do if [ expr$1 % $i -eq 0 ]; then echo$i
expr $1 /$i
fi
i=expr \$i + 1
done | sort -nu
}



## Ursa

This program takes an integer from the command line and outputs its factors.

ursa
decl int n
set n (int args<1>)

decl int i
for (set i 1) (< i (+ (/ n 2) 1)) (inc i)
if (= (mod n i) 0)
out i "  " console
end if
end for
out n endl console


## Ursala

The simple way:

Ursala
#import std
#import nat

factors "n" = (filter not remainder/"n") nrange(1,"n")


The complicated way:

Ursala
factors "n" = nleq-<&@s <.~&r,quotient>*= "n"-* (not remainder/"n")*~ nrange(1,root("n",2))


Another idea would be to approximate an upper bound for the square root of "n" with some bit twiddling such as &!*K31 "n", which evaluates to a binary number of all 1's half the width of "n" rounded up, and another would be to use the division function to get the quotient and remainder at the same time. Combining these ideas, losing the dummy variable, and cleaning up some other cruft, we have

Ursala
factors = nleq-<&@rrZPFLs+ ^(~&r,division)^*D/~& nrange/1+ &!*K31


where nleq-<& isn't strictly necessary unless an ordered list is required.

Ursala
#cast %nL

example = factors 100


{{out}}

txt
<1,2,4,5,10,20,25,50,100>


## VBA

vb
Function Factors(x As Integer) As String
Application.Volatile
Dim i As Integer
Dim cooresponding_factors As String
Factors = 1
corresponding_factors = x
For i = 2 To Sqr(x)
If x Mod i = 0 Then
Factors = Factors & ", " & i
If i <> x / i Then corresponding_factors = x / i & ", " & corresponding_factors
End If
Next i
If x <> 1 Then Factors = Factors & ", " & corresponding_factors
End Function


{{out}}

txt
cell formula is "=Factors(840)"
resultant value is "1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840"


## Wortel

wortel
@let {
factors1      &n !-\%%n @to n
factors_tacit @(\\%% !- @to)
[[
!factors1 10
!factors_tacit 100
!factors1 720
]]
}


Returns:
txt
[
[1 2 5 10]
[1 2 4 5 10 20 25 50 100]
[1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720]
]


## XPL0

XPL0
include c:\cxpl\codes;
int     N0, N, F;
[N0:= 1;
repeat  IntOut(0, N0);  Text(0, " = ");
F:= 2;  N:= N0;
repeat  if rem(N/F) = 0 then
[if N # N0 then Text(0, " * ");
IntOut(0, F);
N:= N/F;
]
else F:= F+1;
until   F>N;
if N0=1 then IntOut(0, 1);      \1 = 1
CrLf(0);
N0:= N0+1;
until   KeyHit;
]


{{out}}

txt

1 = 1
2 = 2
3 = 3
4 = 2 * 2
5 = 5
6 = 2 * 3
7 = 7
8 = 2 * 2 * 2
9 = 3 * 3
10 = 2 * 5
11 = 11
12 = 2 * 2 * 3
13 = 13
14 = 2 * 7
15 = 3 * 5
16 = 2 * 2 * 2 * 2
17 = 17
18 = 2 * 3 * 3
. . .
57086 = 2 * 17 * 23 * 73
57087 = 3 * 3 * 6343
57088 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 223
57089 = 57089
57090 = 2 * 3 * 5 * 11 * 173
57091 = 37 * 1543
57092 = 2 * 2 * 7 * 2039
57093 = 3 * 19031
57094 = 2 * 28547
57095 = 5 * 19 * 601
57096 = 2 * 2 * 2 * 3 * 3 * 13 * 61
57097 = 57097



## zkl

{{trans|Chapel}}

zkl
fcn f(n){ (1).pump(n.toFloat().sqrt(), List,
'wrap(m){((n % m)==0) and T(m,n/m) or Void.Skip}) }
fcn g(n){ [[(m); [1..n.toFloat().sqrt()],'{n%m==0}; '{T(m,n/m)} ]] }  // list comprehension


{{out}}

txt

zkl: f(45)
L(L(1,45),L(3,15),L(5,9))

zkl: g(45)
L(L(1,45),L(3,15),L(5,9))



## ZX Spectrum Basic

{{trans|AWK}}

zxbasic
10 INPUT "Enter a number or 0 to exit: ";n
20 IF n=0 THEN STOP
30 PRINT "Factors of ";n;": ";
40 FOR i=1 TO n
50 IF FN m(n,i)=0 THEN PRINT i;" ";
60 NEXT i
70 DEF FN m(a,b)=a-INT (a/b)*b