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{{task|Prime Numbers}}
;Task: Write a program which counts up from '''1''', displaying each number as the multiplication of its prime factors.
For the purpose of this task, '''1''' (unity) may be shown as itself.
;Example: '''2''' is prime, so it would be shown as itself.
'''6''' is not prime; it would be shown as '''<math>2\times3</math>.'''
'''2144''' is not prime; it would be shown as '''.'''
;Related tasks:
- [[prime decomposition]]
- [[factors of an integer]]
- [[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]]
11l
{{trans|C++}}
F get_prime_factors(=li)
I li == 1
R ‘1’
E
V res = ‘’
V f = 2
L
I li % f == 0
res ‘’= f
li /= f
I li == 1
L.break
res ‘’= ‘ x ’
E
f++
R res
L(x) 1..17
print(‘#4: #.’.format(x, get_prime_factors(x)))
print(‘2144: ’get_prime_factors(2144))
{{out}}
1: 1
2: 2
3: 3
4: 2 x 2
5: 5
6: 2 x 3
7: 7
8: 2 x 2 x 2
9: 3 x 3
10: 2 x 5
11: 11
12: 2 x 2 x 3
13: 13
14: 2 x 7
15: 3 x 5
16: 2 x 2 x 2 x 2
17: 17
2144: 2 x 2 x 2 x 2 x 2 x 67
360 Assembly
* Count in factors 24/03/2017
COUNTFAC CSECT assist plig\COUNTFAC
USING COUNTFAC,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
L R6,=F'1' i=1
DO WHILE=(C,R6,LE,=F'40') do i=1 to 40
LR R7,R6 n=i
MVI F,X'01' f=true
MVC PG,=CL80' ' clear buffer
LA R10,PG pgi=0
XDECO R6,XDEC edit i
MVC 0(12,R10),XDEC output i
LA R10,12(R10) pgi=pgi+12
MVC 0(1,R10),=C'=' output '='
LA R10,1(R10) pgi=pgi+1
IF C,R7,EQ,=F'1' THEN if n=1 then
MVI 0(R10),C'1' output n
ELSE , else
LA R8,2 p=2
DO WHILE=(CR,R8,LE,R7) do while p<=n
LR R4,R7 n
SRDA R4,32 ~
DR R4,R8 /p
IF LTR,R4,Z,R4 THEN if n//p=0 then
IF CLI,F,EQ,X'00' THEN if not f then
MVC 0(1,R10),=C'*' output '*'
LA R10,1(R10) pgi=pgi+1
ELSE , else
MVI F,X'00' f=false
ENDIF , endif
CVD R8,PP convert bin p to packed pp
MVC WORK12,MASX12 in fact L13
EDMK WORK12,PP+2 edit and mark
LA R9,WORK12+12 end of string(p)
SR R9,R1 li=lengh(p) {r1 from edmk}
MVC EDIT12,WORK12 L12<-L13
LA R4,EDIT12+12 source+12
SR R4,R9 -lengh(p)
LR R5,R9 lengh(p)
LR R2,R10 target ix
LR R3,R9 lengh(p)
MVCL R2,R4 f=f||p
AR R10,R9 ix=ix+lengh(p)
LR R4,R7 n
SRDA R4,32 ~
DR R4,R8 /p
LR R7,R5 n=n/p
ELSE , else
LA R8,1(R8) p=p+1
ENDIF , endif
ENDDO , enddo while
ENDIF , endif
XPRNT PG,L'PG print buffer
LA R6,1(R6) i++
ENDDO , enddo i
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
F DS X flag first factor
DS 0D alignment for cvd
PP DS PL8 packed CL8
EDIT12 DS CL12 target CL12
WORK12 DS CL13 char CL13
MASX12 DC X'40',9X'20',X'212060' CL13
XDEC DS CL12 temp
PG DS CL80 buffer
YREGS
END COUNTFAC
{{out}}
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
19=19
20=2*2*5
21=3*7
22=2*11
23=23
24=2*2*2*3
25=5*5
26=2*13
27=3*3*3
28=2*2*7
29=29
30=2*3*5
31=31
32=2*2*2*2*2
33=3*11
34=2*17
35=5*7
36=2*2*3*3
37=37
38=2*19
39=3*13
40=2*2*2*5
```
## Ada
The solution uses the generic package Prime_Numbers from [[Prime decomposition#Ada]]
;count.adb:
```Ada
with Ada.Command_Line, Ada.Text_IO, Prime_Numbers;
procedure Count is
package Prime_Nums is new Prime_Numbers
(Number => Natural, Zero => 0, One => 1, Two => 2); use Prime_Nums;
procedure Put (List : Number_List) is
begin
for Index in List'Range loop
Ada.Text_IO.Put (Integer'Image (List (Index)));
if Index /= List'Last then
Ada.Text_IO.Put (" x");
end if;
end loop;
end Put;
N : Natural := 1;
Max_N : Natural := 15; -- the default for Max_N
begin
if Ada.Command_Line.Argument_Count = 1 then -- read Max_N from command line
Max_N := Integer'Value (Ada.Command_Line.Argument (1));
end if; -- else use the default
loop
Ada.Text_IO.Put (Integer'Image (N) & ": ");
Put (Decompose (N));
Ada.Text_IO.New_Line;
N := N + 1;
exit when N > Max_N;
end loop;
end Count;
```
{{out}}
```txt
1: 1
2: 2
3: 3
4: 2 x 2
5: 5
6: 2 x 3
7: 7
8: 2 x 2 x 2
9: 3 x 3
10: 2 x 5
11: 11
12: 2 x 2 x 3
13: 13
14: 2 x 7
15: 3 x 5
```
## ALGOL 68
{{trans|Euphoria}}
```ALGOL68
OP +:= = (REF FLEX []INT a, INT b) VOID:
BEGIN
[⌈a + 1] INT c;
c[:⌈a] := a;
c[⌈a+1:] := b;
a := c
END;
PROC factorize = (INT nn) []INT:
BEGIN
IF nn = 1 THEN (1)
ELSE
INT k := 2, n := nn;
FLEX[0]INT result;
WHILE n > 1 DO
WHILE n MOD k = 0 DO
result +:= k;
n := n % k
OD;
k +:= 1
OD;
result
FI
END;
FLEX[0]INT factors;
FOR i TO 22 DO
factors := factorize (i);
print ((whole (i, 0), " = "));
FOR j TO UPB factors DO
(j /= 1 | print (" × "));
print ((whole (factors[j], 0)))
OD;
print ((new line))
OD
```
{{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
19 = 19
20 = 2 × 2 × 5
21 = 3 × 7
22 = 2 × 11
```
## AutoHotkey
{{trans|D}}
```AutoHotkey
factorize(n){
if n = 1
return 1
if n < 1
return false
result := 0, m := n, k := 2
While n >= k{
while !Mod(m, k){
result .= " * " . k, m /= k
}
k++
}
return SubStr(result, 5)
}
Loop 22
out .= A_Index ": " factorize(A_index) "`n"
MsgBox % out
```
{{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
19: 19
20: 2 * 2 * 5
21: 3 * 7
22: 2 * 11
```
## AWK
```AWK
# syntax: GAWK -f COUNT_IN_FACTORS.AWK
BEGIN {
fmt = "%d=%s\n"
for (i=1; i<=16; i++) {
printf(fmt,i,factors(i))
}
i = 2144; printf(fmt,i,factors(i))
i = 6358; printf(fmt,i,factors(i))
exit(0)
}
function factors(n, f,p) {
if (n == 1) {
return(1)
}
p = 2
while (p <= n) {
if (n % p == 0) {
f = sprintf("%s%s*",f,p)
n /= p
}
else {
p++
}
}
return(substr(f,1,length(f)-1))
}
```
output:
```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
2144=2*2*2*2*2*67
6358=2*11*17*17
```
## BBC BASIC
```bbcbasic
FOR i% = 1 TO 20
PRINT i% " = " FNfactors(i%)
NEXT
END
DEF FNfactors(N%)
LOCAL P%, f$
IF N% = 1 THEN = "1"
P% = 2
WHILE P% <= N%
IF (N% MOD P%) = 0 THEN
f$ += STR$(P%) + " x "
N% DIV= P%
ELSE
P% += 1
ENDIF
ENDWHILE
= LEFT$(f$, LEN(f$) - 3)
```
Output:
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17 = 17
18 = 2 x 3 x 3
19 = 19
20 = 2 x 2 x 5
```
## Befunge
Lists the first 100 entries in the sequence. If you wish to extend that, the upper limit is implementation dependent, but may be as low as 130 for an interpreter with signed 8 bit data cells (131 is the first prime outside that range).
```befunge>1>>>
:.48*"=",,::1-#v_.v
$<<<^_@#-"e":+1,+55$2<<<
v4_^#-1:/.:g00_00g1+>>0v
>8*"x",,:00g%!^!%g00:p0<
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
.
.
.
```
## C
Code includes a dynamically extending prime number list. The program doesn't stop until you kill it, or it runs out of memory, or it overflows.
```c
#include
#include
typedef unsigned long long ULONG;
ULONG get_prime(int idx)
{
static long n_primes = 0, alloc = 0;
static ULONG *primes = 0;
ULONG last, p;
int i;
if (idx >= n_primes) {
if (n_primes >= alloc) {
alloc += 16; /* be conservative */
primes = realloc(primes, sizeof(ULONG) * alloc);
}
if (!n_primes) {
primes[0] = 2;
primes[1] = 3;
n_primes = 2;
}
last = primes[n_primes-1];
while (idx >= n_primes) {
last += 2;
for (i = 0; i < n_primes; i++) {
p = primes[i];
if (p * p > last) {
primes[n_primes++] = last;
break;
}
if (last % p == 0) break;
}
}
}
return primes[idx];
}
int main()
{
ULONG n, x, p;
int i, first;
for (x = 1; ; x++) {
printf("%lld = ", n = x);
for (i = 0, first = 1; ; i++) {
p = get_prime(i);
while (n % p == 0) {
n /= p;
if (!first) printf(" x ");
first = 0;
printf("%lld", p);
}
if (n <= p * p) break;
}
if (first) printf("%lld\n", n);
else if (n > 1) printf(" x %lld\n", n);
else printf("\n");
}
return 0;
}
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
.
.
.
```
## C++
```Cpp
#include
#include
#include
using namespace std;
void getPrimeFactors( int li )
{
int f = 2; string res;
if( li == 1 ) res = "1";
else
{
while( true )
{
if( !( li % f ) )
{
stringstream ss; ss << f;
res += ss.str();
li /= f; if( li == 1 ) break;
res += " x ";
}
else f++;
}
}
cout << res << "\n";
}
int main( int argc, char* argv[] )
{
for( int x = 1; x < 101; x++ )
{
cout << right << setw( 4 ) << x << ": ";
getPrimeFactors( x );
}
cout << 2144 << ": "; getPrimeFactors( 2144 );
cout << "\n\n";
return system( "pause" );
}
```
{{out}}
```txt
1: 1
2: 2
3: 3
4: 2 x 2
5: 5
6: 2 x 3
7: 7
8: 2 x 2 x 2
9: 3 x 3
10: 2 x 5
11: 11
12: 2 x 2 x 3
13: 13
14: 2 x 7
15: 3 x 5
16: 2 x 2 x 2 x 2
17: 17
18: 2 x 3 x 3
19: 19
20: 2 x 2 x 5
21: 3 x 7
22: 2 x 11
23: 23
24: 2 x 2 x 2 x 3
.
.
.
```
## C#
```c#
using System;
using System.Collections.Generic;
namespace prog
{
class MainClass
{
public static void Main (string[] args)
{
for( int i=1; i<=22; i++ )
{
List f = Factorize(i);
Console.Write( i + ": " + f[0] );
for( int j=1; j Factorize( int n )
{
List l = new List();
if ( n == 1 )
{
l.Add(1);
}
else
{
int k = 2;
while( n > 1 )
{
while( n % k == 0 )
{
l.Add( k );
n /= k;
}
k++;
}
}
return l;
}
}
}
```
## Clojure
```lisp
(ns listfactors
(:gen-class))
(defn factors
"Return a list of factors of N."
([n]
(factors n 2 ()))
([n k acc]
(cond
(= n 1) (if (empty? acc)
[n]
(sort acc))
(>= k n) (if (empty? acc)
[n]
(sort (cons n acc)))
(= 0 (rem n k)) (recur (quot n k) k (cons k acc))
:else (recur n (inc k) acc))))
(doseq [q (range 1 26)]
(println q " = " (clojure.string/join " x "(factors q))))
```
{{Output}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17 = 17
18 = 2 x 3 x 3
19 = 19
20 = 2 x 2 x 5
21 = 3 x 7
22 = 2 x 11
23 = 23
24 = 2 x 2 x 2 x 3
25 = 5 x 5
```
## CoffeeScript
```coffeescript
count_primes = (max) ->
# Count through the natural numbers and give their prime
# factorization. This algorithm uses no division.
# Instead, each prime number starts a rolling odometer
# to help subsequent factorizations. The algorithm works similar
# to the Sieve of Eratosthenes, as we note when each prime number's
# odometer rolls a digit. (As it turns out, as long as your computer
# is not horribly slow at division, you're better off just doing simple
# prime factorizations on each new n vs. using this algorithm.)
console.log "1 = 1"
primes = []
n = 2
while n <= max
factors = []
for prime_odometer in primes
# digits are an array w/least significant digit in
# position 0; for example, [3, [0]] will roll as
# follows:
# [0] -> [1] -> [2] -> [0, 1]
[base, digits] = prime_odometer
i = 0
while true
digits[i] += 1
break if digits[i] < base
digits[i] = 0
factors.push base
i += 1
if i >= digits.length
digits.push 0
if factors.length == 0
primes.push [n, [0, 1]]
factors.push n
console.log "#{n} = #{factors.join('*')}"
n += 1
primes.length
num_primes = count_primes 10000
console.log num_primes
```
## Common Lisp
Auto extending prime list:
```lisp
(defparameter *primes*
(make-array 10 :adjustable t :fill-pointer 0 :element-type 'integer))
(mapc #'(lambda (x) (vector-push x *primes*)) '(2 3 5 7))
(defun extend-primes (n)
(let ((p (+ 2 (elt *primes* (1- (length *primes*))))))
(loop for i = p then (+ 2 i)
while (<= (* i i) n) do
(if (primep i t) (vector-push-extend i *primes*)))))
(defun primep (n &optional skip)
(if (not skip) (extend-primes n))
(if (= n 1) nil
(loop for p across *primes* while (<= (* p p) n)
never (zerop (mod n p)))))
(defun factors (n)
(extend-primes n)
(loop with res for x across *primes* while (> n (* x x)) do
(loop while (zerop (rem n x)) do
(setf n (/ n x))
(push x res))
finally (return (if (> n 1) (cons n res) res))))
(loop for n from 1 do
(format t "~a: ~{~a~^ × ~}~%" n (reverse (factors n))))
```
{{out}}
```txt
1:
2: 2
3: 3
4: 4
5: 5
6: 2 × 3
7: 7
8: 2 × 2 × 2
9: 9
10: 2 × 5
11: 11
12: 2 × 2 × 3
13: 13
14: 2 × 7
...
```
Without saving the primes, and not all that much slower (probably because above code was not well-written):
```lisp
(defun factors (n)
(loop with res for x from 2 to (isqrt n) do
(loop while (zerop (rem n x)) do
(setf n (/ n x))
(push x res))
finally (return (if (> n 1) (cons n res) res))))
(loop for n from 1 do
(format t "~a: ~{~a~^ × ~}~%" n (reverse (factors n))))
```
## D
```d
int[] factorize(in int n) pure nothrow
in {
assert(n > 0);
} body {
if (n == 1) return [1];
int[] result;
int m = n, k = 2;
while (n >= k) {
while (m % k == 0) {
result ~= k;
m /= k;
}
k++;
}
return result;
}
void main() {
import std.stdio;
foreach (i; 1 .. 22)
writefln("%d: %(%d × %)", i, i.factorize());
}
```
{{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
19: 19
20: 2 × 2 × 5
21: 3 × 7
```
### Alternative Version
{{libheader|uiprimes}} Library ''uiprimes'' is a homebrew library to generate prime numbers upto the maximum 32bit unsigned integer range 2^32-1, by using a pre-generated bit array of [[Sieve of Eratosthenes]] (a dll in size of ~256M bytes :p ).
```d
import std.stdio, std.math, std.conv, std.algorithm,
std.array, std.string, import xt.uiprimes;
pragma(lib, "uiprimes.lib");
// function _factorize_ included in uiprimes.lib
ulong[] factorize(ulong n) {
if (n == 0) return [];
if (n == 1) return [1];
ulong[] res;
uint limit = cast(uint)(1 + sqrt(n));
foreach (p; Primes(limit)) {
if (n == 1) break;
if (0UL == (n % p))
while((n > 1) && (0UL == (n % p ))) {
res ~= p;
n /= p;
}
}
if (n > 1)
res ~= [n];
return res;
}
string productStr(T)(in T[] nums) {
return nums.map!text().join(" x ");
}
void main() {
foreach (i; 1 .. 21)
writefln("%2d = %s", i, productStr(factorize(i)));
}
```
## DCL
Assumes file primes.txt is a list of prime numbers;
```DCL
$ close /nolog primes
$ on control_y then $ goto clean
$
$ n = 1
$ outer_loop:
$ x = n
$ open primes primes.txt
$
$ loop1:
$ read /end_of_file = prime primes prime
$ prime = f$integer( prime )
$ loop2:
$ t = x / prime
$ if t * prime .eq. x
$ then
$ if f$type( factorization ) .eqs. ""
$ then
$ factorization = f$string( prime )
$ else
$ factorization = factorization + "*" + f$string( prime )
$ endif
$ if t .eq. 1 then $ goto done
$ x = t
$ goto loop2
$ else
$ goto loop1
$ endif
$ prime:
$ if f$type( factorization ) .eqs. ""
$ then
$ factorization = f$string( x )
$ else
$ factorization = factorization + "*" + f$string( x )
$ endif
$ done:
$ write sys$output f$fao( "!4SL = ", n ), factorization
$ delete /symbol factorization
$ close primes
$ n = n + 1
$ if n .le. 2144 then $ goto outer_loop
$ exit
$
$ clean:
$ close /nolog primes
```
{{out}}
```txt
$ @count_in_factors
1 = 1
2 = 2
3 = 3
4 = 2*2
5 = 5
6 = 2*3
...
2144 = 2*2*2*2*2*67
```
## DWScript
```delphi
function Factorize(n : Integer) : String;
begin
if n <= 1 then
Exit('1');
var k := 2;
while n >= k do begin
while (n mod k) = 0 do begin
Result += ' * '+IntToStr(k);
n := n div k;
end;
Inc(k);
end;
Result:=SubStr(Result, 4);
end;
var i : Integer;
for i := 1 to 22 do
PrintLn(IntToStr(i) + ': ' + Factorize(i));
```
{{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
19: 19
20: 2 * 2 * 5
21: 3 * 7
22: 2 * 11
```
## EchoLisp
```scheme
(define (task (nfrom 2) (range 20))
(for ((i (in-range nfrom (+ nfrom range))))
(writeln i "=" (string-join (prime-factors i) " x "))))
```
{{out}}
```txt
(task 1_000_000_000)
1000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
1000000001 = 7 x 11 x 13 x 19 x 52579
1000000002 = 2 x 3 x 43 x 983 x 3943
1000000003 = 23 x 307 x 141623
1000000004 = 2 x 2 x 41 x 41 x 148721
1000000005 = 3 x 5 x 66666667
1000000006 = 2 x 500000003
1000000007 = 1000000007
1000000008 = 2 x 2 x 2 x 3 x 3 x 7 x 109 x 109 x 167
1000000009 = 1000000009
1000000010 = 2 x 5 x 17 x 5882353
1000000011 = 3 x 29 x 11494253
1000000012 = 2 x 2 x 11 x 47 x 79 x 6121
1000000013 = 7699 x 129887
1000000014 = 2 x 3 x 13 x 103 x 124471
1000000015 = 5 x 7 x 31 x 223 x 4133
1000000016 = 2 x 2 x 2 x 2 x 62500001
1000000017 = 3 x 3 x 111111113
1000000018 = 2 x 500000009
1000000019 = 83 x 12048193
```
## Eiffel
```Eiffel
class
COUNT_IN_FACTORS
feature
display_factor (p: INTEGER)
-- Factors of all integers up to 'p'.
require
p_positive: p > 0
local
factors: ARRAY [INTEGER]
do
across
1 |..| p as c
loop
io.new_line
io.put_string (c.item.out + "%T")
factors := factor (c.item)
across
factors as f
loop
io.put_integer (f.item)
if f.is_last = False then
io.put_string (" x ")
end
end
end
end
factor (p: INTEGER): ARRAY [INTEGER]
-- Prime decomposition of 'p'.
require
p_positive: p > 0
local
div, i, next, rest: INTEGER
do
create Result.make_empty
if p = 1 then
Result.force (1, 1)
end
div := 2
next := 3
rest := p
from
i := 1
until
rest = 1
loop
from
until
rest \\ div /= 0
loop
Result.force (div, i)
rest := (rest / div).floor
i := i + 1
end
div := next
next := next + 2
end
ensure
is_divisor: across Result as r all p \\ r.item = 0 end
end
end
```
Test Output:
```txt
1 1
2 2
3 3
4 2 x 2
5 5
6 2 x 3
7 7
8 2 x 2 x 2
9 3 x 3
10 2 x 5
...
4990 2 x 5 x 499
4991 7 x 23 x 31
4992 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13
4993 4993
4994 2 x 11 x 227
4995 3 x 3 x 3 x 5 x 37
4996 2 x 2 x 1249
4997 19 x 263
4998 2 x 3 x 7 x 7 x 17
4999 4999
5000 2 x 2 x 2 x 5 x 5 x 5 x 5
```
## Elixir
```elixir
defmodule RC do
def factor(n), do: factor(n, 2, [])
def factor(n, i, fact) when n < i*i, do: Enum.reverse([n|fact])
def factor(n, i, fact) do
if rem(n,i)==0, do: factor(div(n,i), i, [i|fact]),
else: factor(n, i+1, fact)
end
end
Enum.each(1..20, fn n ->
IO.puts "#{n}: #{Enum.join(RC.factor(n)," x ")}" end)
```
{{out}}
```txt
1: 1
2: 2
3: 3
4: 2 x 2
5: 5
6: 2 x 3
7: 7
8: 2 x 2 x 2
9: 3 x 3
10: 2 x 5
11: 11
12: 2 x 2 x 3
13: 13
14: 2 x 7
15: 3 x 5
16: 2 x 2 x 2 x 2
17: 17
18: 2 x 3 x 3
19: 19
20: 2 x 2 x 5
```
## Euphoria
```euphoria
function factorize(integer n)
sequence result
integer k
if n = 1 then
return {1}
else
k = 2
result = {}
while n > 1 do
while remainder(n, k) = 0 do
result &= k
n /= k
end while
k += 1
end while
return result
end if
end function
sequence factors
for i = 1 to 22 do
printf(1, "%d: ", i)
factors = factorize(i)
for j = 1 to length(factors)-1 do
printf(1, "%d * ", factors[j])
end for
printf(1, "%d\n", factors[$])
end for
```
{{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
19: 19
20: 2 * 2 * 5
21: 3 * 7
22: 2 * 11
```
=={{header|F_Sharp|F#}}==
```fsharp
let factorsOf (num) =
Seq.unfold (fun (f, n) ->
let rec genFactor (f, n) =
if f > n then None
elif n % f = 0 then Some (f, (f, n/f))
else genFactor (f+1, n)
genFactor (f, n)) (2, num)
let showLines = Seq.concat (seq { yield seq{ yield(Seq.singleton 1)}; yield (Seq.skip 2 (Seq.initInfinite factorsOf))})
showLines |> Seq.iteri (fun i f -> printfn "%d = %s" (i+1) (String.Join(" * ", Seq.toArray f)))
```
{{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
:
2140 = 2 * 2 * 5 * 107
2141 = 2141
2142 = 2 * 3 * 3 * 7 * 17
2143 = 2143
2144 = 2 * 2 * 2 * 2 * 2 * 67
2145 = 3 * 5 * 11 * 13
2146 = 2 * 29 * 37
2147 = 19 * 113
:
```
## Factor
```factor
USING: math.parser math.primes.factors math.ranges ;
IN: scratchpad "1: 1" print 2 20 [a,b] [ dup pprint ": " write factors [ number>string ] map " x " join print ] each
```
{{out}}
```txt
1: 1
2: 2
3: 3
4: 2 x 2
5: 5
6: 2 x 3
7: 7
8: 2 x 2 x 2
9: 3 x 3
10: 2 x 5
11: 11
12: 2 x 2 x 3
13: 13
14: 2 x 7
15: 3 x 5
16: 2 x 2 x 2 x 2
17: 17
18: 2 x 3 x 3
19: 19
20: 2 x 2 x 5
```
## Forth
```forth
: .factors ( n -- )
2
begin 2dup dup * >=
while 2dup /mod swap
if drop 1+ 1 or \ next odd number
else -rot nip dup . ." x "
then
repeat
drop . ;
: main ( n -- )
." 1 : 1" cr
1+ 2 ?do i . ." : " i .factors cr loop ;
15 main bye
```
## Fortran
Please find the example output along with the build instructions in the comments at the start of the FORTRAN 2008 source. Compiler: gfortran from the GNU compiler collection. Command interpreter: bash. The code writes j assertions which don't prove primality of the factors but does prove they are the factors.
This algorithm creates a sieve of Eratosthenes, storing the largest prime factor to mark composites. It then finds prime factors by repeatedly looking up the value in the sieve, then dividing by the factor found until the value is itself prime. Using the sieve table to store factors rather than as a plain bitmap was to me a novel idea.
```FORTRAN
!-*- mode: compilation; default-directory: "/tmp/" -*-
!Compilation started at Thu Jun 6 23:29:06
!
!a=./f && make $a && echo -2 | OMP_NUM_THREADS=2 $a
!gfortran -std=f2008 -Wall -fopenmp -ffree-form -fall-intrinsics -fimplicit-none f.f08 -o f
! assert 1 = */ 1
! assert 2 = */ 2
! assert 3 = */ 3
! assert 4 = */ 2 2
! assert 5 = */ 5
! assert 6 = */ 2 3
! assert 7 = */ 7
! assert 8 = */ 2 2 2
! assert 9 = */ 3 3
! assert 10 = */ 2 5
! assert 11 = */ 11
! assert 12 = */ 3 2 2
! assert 13 = */ 13
! assert 14 = */ 2 7
! assert 15 = */ 3 5
! assert 16 = */ 2 2 2 2
! assert 17 = */ 17
! assert 18 = */ 3 2 3
! assert 19 = */ 19
! assert 20 = */ 2 2 5
! assert 21 = */ 3 7
! assert 22 = */ 2 11
! assert 23 = */ 23
! assert 24 = */ 3 2 2 2
! assert 25 = */ 5 5
! assert 26 = */ 2 13
! assert 27 = */ 3 3 3
! assert 28 = */ 2 2 7
! assert 29 = */ 29
! assert 30 = */ 5 2 3
! assert 31 = */ 31
! assert 32 = */ 2 2 2 2 2
! assert 33 = */ 3 11
! assert 34 = */ 2 17
! assert 35 = */ 5 7
! assert 36 = */ 3 3 2 2
! assert 37 = */ 37
! assert 38 = */ 2 19
! assert 39 = */ 3 13
! assert 40 = */ 5 2 2 2
module prime_mod
! sieve_table stores 0 in prime numbers, and a prime factor in composites.
integer, dimension(:), allocatable :: sieve_table
private :: PrimeQ
contains
! setup routine must be called first!
subroutine sieve(n) ! populate sieve_table. If n is 0 it deallocates storage, invalidating sieve_table.
integer, intent(in) :: n
integer :: status, i, j
if ((n .lt. 1) .or. allocated(sieve_table)) deallocate(sieve_table)
if (n .lt. 1) return
allocate(sieve_table(n), stat=status)
if (status .ne. 0) stop 'cannot allocate space'
sieve_table(1) = 1
do i=2,int(sqrt(real(n)))+1
if (sieve_table(i) .eq. 0) then
do j = i*i, n, i
sieve_table(j) = i
end do
end if
end do
end subroutine sieve
subroutine check_sieve(n)
integer, intent(in) :: n
if (.not. (allocated(sieve_table) .and. ((1 .le. n) .and. (n .le. size(sieve_table))))) stop 'Call sieve first'
end subroutine check_sieve
logical function isPrime(p)
integer, intent(in) :: p
call check_sieve(p)
isPrime = PrimeQ(p)
end function isPrime
logical function isComposite(p)
integer, intent(in) :: p
isComposite = .not. isPrime(p)
end function isComposite
logical function PrimeQ(p)
integer, intent(in) :: p
PrimeQ = sieve_table(p) .eq. 0
end function PrimeQ
subroutine prime_factors(p, rv, n)
integer, intent(in) :: p ! number to factor
integer, dimension(:), intent(out) :: rv ! the prime factors
integer, intent(out) :: n ! number of factors returned
integer :: i, m
call check_sieve(p)
m = p
i = 1
if (p .ne. 1) then
do while ((.not. PrimeQ(m)) .and. (i .lt. size(rv)))
rv(i) = sieve_table(m)
m = m/rv(i)
i = i+1
end do
end if
if (i .le. size(rv)) rv(i) = m
n = i
end subroutine prime_factors
end module prime_mod
program count_in_factors
use prime_mod
integer :: i, n
integer, dimension(8) :: factors
call sieve(40) ! setup
do i=1,40
factors = 0
call prime_factors(i, factors, n)
write(6,*)'assert',i,'= */',factors(:n)
end do
call sieve(0) ! release memory
end program count_in_factors
```
## FreeBASIC
```freebasic
' FB 1.05.0 Win64
Sub getPrimeFactors(factors() As UInteger, n As UInteger)
If n < 2 Then Return
Dim factor As UInteger = 2
Do
If n Mod factor = 0 Then
Redim Preserve factors(0 To UBound(factors) + 1)
factors(UBound(factors)) = factor
n \= factor
If n = 1 Then Return
Else
factor += 1
End If
Loop
End Sub
Dim factors() As UInteger
For i As UInteger = 1 To 20
Print Using "##"; i;
Print " = ";
If i > 1 Then
Erase factors
getPrimeFactors factors(), i
For j As Integer = LBound(factors) To UBound(factors)
Print factors(j);
If j < UBound(factors) Then Print " x ";
Next j
Print
Else
Print i
End If
Next i
Print
Print "Press any key to quit"
Sleep
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17 = 17
18 = 2 x 3 x 3
19 = 19
20 = 2 x 2 x 5
```
## Frink
Frink's factoring routines work on arbitrarily-large integers.
```frink
i = 1
while true
{
println[join[" x ", factorFlat[i]]]
i = i + 1
}
```
## Go
```go
package main
import "fmt"
func main() {
fmt.Println("1: 1")
for i := 2; ; i++ {
fmt.Printf("%d: ", i)
var x string
for n, f := i, 2; n != 1; f++ {
for m := n % f; m == 0; m = n % f {
fmt.Print(x, f)
x = "×"
n /= f
}
}
fmt.Println()
}
}
```
{{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
...
```
## Groovy
```groovy
def factors(number) {
if (number == 1) {
return [1]
}
def factors = []
BigInteger value = number
BigInteger possibleFactor = 2
while (possibleFactor <= value) {
if (value % possibleFactor == 0) {
factors << possibleFactor
value /= possibleFactor
} else {
possibleFactor++
}
}
factors
}
Number.metaClass.factors = { factors(delegate) }
((1..10) + (6351..6359)).each { number ->
println "$number = ${number.factors().join(' x ')}"
}
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
6351 = 3 x 29 x 73
6352 = 2 x 2 x 2 x 2 x 397
6353 = 6353
6354 = 2 x 3 x 3 x 353
6355 = 5 x 31 x 41
6356 = 2 x 2 x 7 x 227
6357 = 3 x 13 x 163
6358 = 2 x 11 x 17 x 17
6359 = 6359
```
## Haskell
Using factorize function from the [[Prime_decomposition#Haskell|prime decomposition]] task,
```haskell
import Data.List (intercalate)
showFactors n = show n ++ " = " ++ (intercalate " * " . map show . factorize) n
-- Pointfree form
showFactors = ((++) . show) <*> ((" = " ++) . intercalate " * " . map show . factorize)
```
isPrime n = n > 1 && noDivsBy primeNums n
{{out}}
```haskell>Main> print 1 >
mapM_ (putStrLn . showFactors) [2..]
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
. . .
Main> mapM_ (putStrLn . showFactors) [2144..]
2144 = 2 * 2 * 2 * 2 * 2 * 67
2145 = 3 * 5 * 11 * 13
2146 = 2 * 29 * 37
2147 = 19 * 113
2148 = 2 * 2 * 3 * 179
2149 = 7 * 307
2150 = 2 * 5 * 5 * 43
2151 = 3 * 3 * 239
2152 = 2 * 2 * 2 * 269
2153 = 2153
2154 = 2 * 3 * 359
. . .
Main> mapM_ (putStrLn . showFactors) [121231231232155..]
121231231232155 = 5 * 11 * 419 * 5260630559
121231231232156 = 2 * 2 * 97 * 1061 * 294487867
121231231232157 = 3 * 3 * 3 * 131 * 34275157261
121231231232158 = 2 * 19 * 67 * 1231 * 38681033
121231231232159 = 121231231232159
121231231232160 = 2 * 2 * 2 * 2 * 2 * 3 * 5 * 7 * 7 * 5154389083
121231231232161 = 121231231232161
121231231232162 = 2 * 60615615616081
121231231232163 = 3 * 13 * 83 * 191089 * 195991
121231231232164 = 2 * 2 * 253811 * 119410931
121231231232165 = 5 * 137 * 176979899609
. . .
```
The real solution seems to have to be some sort of a segmented offset sieve of Eratosthenes, storing factors in array's cells instead of just marks. That way the speed of production might not be diminishing as much.
=={{header|Icon}} and {{header|Unicon}}==
```Icon
procedure main()
write("Press ^C to terminate")
every f := [i:= 1] | factors(i := seq(2)) do {
writes(i," : [")
every writes(" ",!f|"]\n")
}
end
link factors
```
{{libheader|Icon Programming Library}}
[http://www.cs.arizona.edu/icon/library/src/procs/factors.icn factors.icn provides factors]
{{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 ]
...
```
=={{header|IS-BASIC}}==
100 PROGRAM "Factors.bas"
110 FOR I=1 TO 30
120 PRINT I;"= ";FACTORS$(I)
130 NEXT
140 DEF FACTORS$(N)
150 LET F$=""
160 IF N=1 THEN
170 LET FACTORS$="1"
180 ELSE
190 LET P=2
200 DO WHILE P<=N
210 IF MOD(N,P)=0 THEN
220 LET F$=F$&STR$(P)&"*"
230 LET N=INT(N/P)
240 ELSE
250 LET P=P+1
260 END IF
270 LOOP
280 LET FACTORS$=F$(1:LEN(F$)-1)
290 END IF
300 END DEF
```
{{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
19 = 19
20 = 2*2*5
21 = 3*7
22 = 2*11
23 = 23
24 = 2*2*2*3
25 = 5*5
26 = 2*13
27 = 3*3*3
28 = 2*2*7
29 = 29
30 = 2*3*5
```
## J
'''Solution''':Use J's factoring primitive,
```j>q: ,"1 ': ',"1 ":@q:) 2+i.10
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
```
## Java
{{trans|Visual Basic .NET}}
```java
public class CountingInFactors{
public static void main(String[] args){
for(int i = 1; i<= 10; i++){
System.out.println(i + " = "+ countInFactors(i));
}
for(int i = 9991; i <= 10000; i++){
System.out.println(i + " = "+ countInFactors(i));
}
}
private static String countInFactors(int n){
if(n == 1) return "1";
StringBuilder sb = new StringBuilder();
n = checkFactor(2, n, sb);
if(n == 1) return sb.toString();
n = checkFactor(3, n, sb);
if(n == 1) return sb.toString();
for(int i = 5; i <= n; i+= 2){
if(i % 3 == 0)continue;
n = checkFactor(i, n, sb);
if(n == 1)break;
}
return sb.toString();
}
private static int checkFactor(int mult, int n, StringBuilder sb){
while(n % mult == 0 ){
if(sb.length() > 0) sb.append(" x ");
sb.append(mult);
n /= mult;
}
return n;
}
}
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
9991 = 97 x 103
9992 = 2 x 2 x 2 x 1249
9993 = 3 x 3331
9994 = 2 x 19 x 263
9995 = 5 x 1999
9996 = 2 x 2 x 3 x 7 x 7 x 17
9997 = 13 x 769
9998 = 2 x 4999
9999 = 3 x 3 x 11 x 101
10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
```
## JavaScript
```javascript
for(i = 1; i <= 10; i++)
console.log(i + " : " + factor(i).join(" x "));
function factor(n) {
var factors = [];
if (n == 1) return [1];
for(p = 2; p <= n; ) {
if((n % p) == 0) {
factors[factors.length] = p;
n /= p;
}
else p++;
}
return factors;
}
```
{{out}}
```txt
1 : 1
2 : 2
3 : 3
4 : 2 x 2
5 : 5
6 : 2 x 3
7 : 7
8 : 2 x 2 x 2
9 : 3 x 3
10 : 2 x 5
```
## Julia
```julia
using Primes, Printf
function strfactor(n::Integer)
n > -2 || return "-1 × " * strfactor(-n)
isprime(n) || n < 2 && return dec(n)
f = factor(Vector{typeof(n)}, n)
return join(f, " × ")
end
lo, hi = -4, 40
println("Factor print $lo to $hi:")
for n in lo:hi
@printf("%5d = %s\n", n, strfactor(n))
end
```
{{out}}
```txt
Factor print -4 to 40:
-4 = -1 × 2 × 2
-3 = -1 × 3
-2 = -1 × 2
-1 = -1
0 = 0
1 = 1
2 = 2
3 = 3
4 = 2 × 2
5 = 5
6 = 2 × 3
7 = 7
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
11 = 11
12 = 2 × 2 × 3
13 = 13
14 = 2 × 7
15 = 3 × 5
16 = 2 × 2 × 2 × 2
17 = 17
18 = 2 × 3 × 3
19 = 19
20 = 2 × 2 × 5
21 = 3 × 7
22 = 2 × 11
23 = 23
24 = 2 × 2 × 2 × 3
25 = 5 × 5
26 = 2 × 13
27 = 3 × 3 × 3
28 = 2 × 2 × 7
29 = 29
30 = 2 × 3 × 5
31 = 31
32 = 2 × 2 × 2 × 2 × 2
33 = 3 × 11
34 = 2 × 17
35 = 5 × 7
36 = 2 × 2 × 3 × 3
37 = 37
38 = 2 × 19
39 = 3 × 13
40 = 2 × 2 × 2 × 5
```
## Kotlin
```scala
// version 1.1.2
fun isPrime(n: Int) : Boolean {
if (n < 2) return false
if (n % 2 == 0) return n == 2
if (n % 3 == 0) return n == 3
var d = 5
while (d * d <= n) {
if (n % d == 0) return false
d += 2
if (n % d == 0) return false
d += 4
}
return true
}
fun getPrimeFactors(n: Int): List {
val factors = mutableListOf()
if (n < 1) return factors
if (n == 1 || isPrime(n)) {
factors.add(n)
return factors
}
var factor = 2
var nn = n
while (true) {
if (nn % factor == 0) {
factors.add(factor)
nn /= factor
if (nn == 1) return factors
if (isPrime(nn)) factor = nn
}
else if (factor >= 3) factor += 2
else factor = 3
}
}
fun main(args: Array) {
val list = (MutableList(22) { it + 1 } + 2144) + 6358
for (i in list)
println("${"%4d".format(i)} = ${getPrimeFactors(i).joinToString(" * ")}")
}
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 * 2
5 = 5
6 = 2 * 3
7 = 7
8 = 2 * 2 * 2
9 = 3 * 3
10 = 2 * 5
11 = 11
12 = 2 * 2 * 3
13 = 13
14 = 2 * 7
15 = 3 * 5
16 = 2 * 2 * 2 * 2
17 = 17
18 = 2 * 3 * 3
19 = 19
20 = 2 * 2 * 5
21 = 3 * 7
22 = 2 * 11
2144 = 2 * 2 * 2 * 2 * 2 * 67
6358 = 2 * 11 * 17 * 17
```
## Liberty BASIC
```lb
'see Run BASIC solution
for i = 1000 to 1016
print i;" = "; factorial$(i)
next
wait
function factorial$(num)
if num = 1 then factorial$ = "1"
fct = 2
while fct <= num
if (num mod fct) = 0 then
factorial$ = factorial$ ; x$ ; fct
x$ = " x "
num = num / fct
else
fct = fct + 1
end if
wend
end function
```
{{out}}
```txt
1000 = 2 x 2 x 2 x 5 x 5 x 5
1001 = 7 x 11 x 13
1002 = 2 x 3 x 167
1003 = 17 x 59
1004 = 2 x 2 x 251
1005 = 3 x 5 x 67
1006 = 2 x 503
1007 = 19 x 53
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
1009 = 1009
1010 = 2 x 5 x 101
1011 = 3 x 337
1012 = 2 x 2 x 11 x 23
1013 = 1013
1014 = 2 x 3 x 13 x 13
1015 = 5 x 7 x 29
1016 = 2 x 2 x 2 x 127
```
## Lua
```Lua
function factorize( n )
if n == 1 then return {1} end
local k = 2
res = {}
while n > 1 do
while n % k == 0 do
res[#res+1] = k
n = n / k
end
k = k + 1
end
return res
end
for i = 1, 22 do
io.write( i, ": " )
fac = factorize( i )
io.write( fac[1] )
for j = 2, #fac do
io.write( " * ", fac[j] )
end
print ""
end
```
## M2000 Interpreter
Decompose function now return array (in number decomposition task return an inventory list).
```M2000 Interpreter
Module Count_in_factors {
Inventory Known1=2@, 3@
IsPrime=lambda Known1 (x as decimal) -> {
=0=1
if exist(Known1, x) then =1=1 : exit
if x<=5 OR frac(x) then {if x == 2 OR x == 3 OR x == 5 then Append Known1, x : =1=1
Break}
if frac(x/2) else exit
if frac(x/3) else exit
x1=sqrt(x):d = 5@
{if frac(x/d ) else exit
d += 2: if d>x1 then Append Known1, x : =1=1 : exit
if frac(x/d) else exit
d += 4: if d<= x1 else Append Known1, x : =1=1: exit
loop
}
}
decompose=lambda IsPrime (n as decimal) -> {
Factors=(,)
{
k=2@
While frac(n/k)=0
n/=k
Append Factors, (k,)
End While
if n=1 then exit
k++
While frac(n/k)=0
n/=k
Append Factors, (k,)
End While
if n=1 then exit
{
k+=2
while not isprime(k) {k+=2}
While frac(n/k)=0
n/=k : Append Factors, (k,)
End While
if n=1 then exit
loop
}
}
=Factors
}
fold=lambda (a, f$)->{
Push if$(len(f$)=0->f$, f$+"x")+str$(a,"")
}
Print "1=1"
i=1@
do
i++
Print str$(i,"")+"="+Decompose(i)#fold$(fold,"")
always
}
Count_in_factors
```
## M4
```M4
define(`for',
`ifelse($#,0,``$0'',
`ifelse(eval($2<=$3),1,
`pushdef(`$1',$2)$5`'popdef(`$1')$0(`$1',eval($2+$4),$3,$4,`$5')')')')dnl
define(`by',
`ifelse($1,$2,
$1,
`ifelse(eval($1%$2==0),1,
`$2 x by(eval($1/$2),$2)',
`by($1,eval($2+1))') ') ')dnl
define(`wby',
`$1 = ifelse($1,1,
$1,
`by($1,2)') ')dnl
for(`y',1,25,1, `wby(y)
')
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17 = 17
18 = 2 x 3 x 3
19 = 19
20 = 2 x 2 x 5
21 = 3 x 7
22 = 2 x 11
23 = 23
24 = 2 x 2 x 2 x 3
25 = 5 x 5
```
## Maple
```maple
factorNum := proc(n)
local i, j, firstNum;
if n = 1 then
printf("%a", 1);
end if;
firstNum := true:
for i in ifactors(n)[2] do
for j to i[2] do
if firstNum then
printf ("%a", i[1]);
firstNum := false:
else
printf(" x %a", i[1]);
end if;
end do;
end do;
printf("\n");
return NULL;
end proc:
for i from 1 to 10 do
printf("%2a: ", i);
factorNum(i);
end do;
```
{{out}}
```txt
1: 1
2: 2
3: 3
4: 2 x 2
5: 5
6: 2 x 3
7: 7
8: 2 x 2 x 2
9: 3 x 3
10: 2 x 5
```
=={{header|Mathematica}} / {{header|Wolfram Language}}==
```Mathematica
n = 2;
While[n < 100,
Print[Row[Riffle[Flatten[Map[Apply[ConstantArray, #] &, FactorInteger[n]]],"*"]]];
n++]
```
## NetRexx
{{trans|Java}}
```NetRexx
/* NetRexx */
options replace format comments java crossref symbols nobinary
runSample(arg)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method factor(val) public static
rv = 1
if val > 1 then do
rv = ''
loop n_ = val until n_ = 1
parse checkFactor(2, n_, rv) n_ rv
if n_ = 1 then leave n_
parse checkFactor(3, n_, rv) n_ rv
if n_ = 1 then leave n_
loop m_ = 5 to n_ by 2 until n_ = 1
if m_ // 3 = 0 then iterate m_
parse checkFactor(m_, n_, rv) n_ rv
end m_
end n_
end
return rv
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method checkFactor(mult = long, n_ = long, fac) private static binary
msym = 'x'
loop while n_ // mult = 0
fac = fac msym mult
n_ = n_ % mult
end
fac = (fac.strip).strip('l', msym).space
return n_ fac
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
-- input is a list of pairs of numbers - no checking is done
if arg = '' then arg = '1 11 89 101 1000 1020 10000 10010'
loop while arg \= ''
parse arg lv rv arg
say
say '-'.copies(60)
say lv.right(8) 'to' rv
say '-'.copies(60)
loop fv = lv to rv
fac = factor(fv)
pv = ''
if fac.words = 1 & fac \= 1 then pv = ''
say fv.right(8) '=' fac pv
end fv
end
return
```
{{out}}
------------------------------------------------------------
1 to 11
------------------------------------------------------------
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
------------------------------------------------------------
89 to 101
------------------------------------------------------------
89 = 89
90 = 2 x 3 x 3 x 5
91 = 7 x 13
92 = 2 x 2 x 23
93 = 3 x 31
94 = 2 x 47
95 = 5 x 19
96 = 2 x 2 x 2 x 2 x 2 x 3
97 = 97
98 = 2 x 7 x 7
99 = 3 x 3 x 11
100 = 2 x 2 x 5 x 5
101 = 101
------------------------------------------------------------
1000 to 1020
------------------------------------------------------------
1000 = 2 x 2 x 2 x 5 x 5 x 5
1001 = 7 x 11 x 13
1002 = 2 x 3 x 167
1003 = 17 x 59
1004 = 2 x 2 x 251
1005 = 3 x 5 x 67
1006 = 2 x 503
1007 = 19 x 53
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
1009 = 1009
1010 = 2 x 5 x 101
1011 = 3 x 337
1012 = 2 x 2 x 11 x 23
1013 = 1013
1014 = 2 x 3 x 13 x 13
1015 = 5 x 7 x 29
1016 = 2 x 2 x 2 x 127
1017 = 3 x 3 x 113
1018 = 2 x 509
1019 = 1019
1020 = 2 x 2 x 3 x 5 x 17
------------------------------------------------------------
10000 to 10010
------------------------------------------------------------
10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
10001 = 73 x 137
10002 = 2 x 3 x 1667
10003 = 7 x 1429
10004 = 2 x 2 x 41 x 61
10005 = 3 x 5 x 23 x 29
10006 = 2 x 5003
10007 = 10007
10008 = 2 x 2 x 2 x 3 x 3 x 139
10009 = 10009
10010 = 2 x 5 x 7 x 11 x 13
```
## Nim
{{trans|C}}
```nim
var primes = newSeq[int]()
proc getPrime(idx: int): int =
if idx >= primes.len:
if primes.len == 0:
primes.add 2
primes.add 3
var last = primes[primes.high]
while idx >= primes.len:
last += 2
for i, p in primes:
if p * p > last:
primes.add last
break
if last mod p == 0:
break
return primes[idx]
for x in 1 ..< int32.high.int:
stdout.write x, " = "
var n = x
var first = 1
for i in 0 ..< int32.high:
let p = getPrime(i)
while n mod p == 0:
n = n div p
if first == 0: stdout.write " x "
first = 0
stdout.write p
if n <= p * p:
break
if first > 0: echo n
elif n > 1: echo " x ", n
else: echo ""
```
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
...
```
## Objeck
```objeck
class CountingInFactors {
function : Main(args : String[]) ~ Nil {
for(i := 1; i <= 10; i += 1;){
count := CountInFactors(i);
("{$i} = {$count}")->PrintLine();
};
for(i := 9991; i <= 10000; i += 1;){
count := CountInFactors(i);
("{$i} = {$count}")->PrintLine();
};
}
function : CountInFactors(n : Int) ~ String {
if(n = 1) {
return "1";
};
sb := "";
n := CheckFactor(2, n, sb);
if(n = 1) {
return sb;
};
n := CheckFactor(3, n, sb);
if(n = 1) {
return sb;
};
for(i := 5; i <= n; i += 2;) {
if(i % 3 <> 0) {
n := CheckFactor(i, n, sb);
if(n = 1) {
break;
};
};
};
return sb;
}
function : CheckFactor(mult : Int, n : Int, sb : String) ~ Int {
while(n % mult = 0 ) {
if(sb->Size() > 0) {
sb->Append(" x ");
};
sb->Append(mult);
n /= mult;
};
return n;
}
}
```
Output:
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
9991 = 97 x 103
9992 = 2 x 2 x 2 x 1249
9993 = 3 x 3331
9994 = 2 x 19 x 263
9995 = 5 x 1999
9996 = 2 x 2 x 3 x 7 x 7 x 17
9997 = 13 x 769
9998 = 2 x 4999
9999 = 3 x 3 x 11 x 101
10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
```
## OCaml
```ocaml
open Big_int
let prime_decomposition x =
let rec inner c p =
if lt_big_int p (square_big_int c) then
[p]
else if eq_big_int (mod_big_int p c) zero_big_int then
c :: inner c (div_big_int p c)
else
inner (succ_big_int c) p
in
inner (succ_big_int (succ_big_int zero_big_int)) x
let () =
let rec aux v =
let ps = prime_decomposition v in
print_string (string_of_big_int v);
print_string " = ";
print_endline (String.concat " x " (List.map string_of_big_int ps));
aux (succ_big_int v)
in
aux unit_big_int
```
{{out|Execution}}
```txt
$ ocamlopt -o count.opt nums.cmxa count.ml
$ ./count.opt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
...
6351 = 3 x 29 x 73
6352 = 2 x 2 x 2 x 2 x 397
6353 = 6353
6354 = 2 x 3 x 3 x 353
6355 = 5 x 31 x 41
6356 = 2 x 2 x 7 x 227
6357 = 3 x 13 x 163
6358 = 2 x 11 x 17 x 17
6359 = 6359
^C
```
## Octave
Octave's factor function returns an array:
```octave
for (n = 1:20)
printf ("%i: ", n)
printf ("%i ", factor (n))
printf ("\n")
endfor
```
{{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
19: 19
20: 2 2 5
```
## PARI/GP
```parigp
fnice(n)={
my(f,s="",s1);
if (n < 2, return(n));
f = factor(n);
s = Str(s, f[1,1]);
if (f[1, 2] != 1, s=Str(s, "^", f[1,2]));
for(i=2,#f[,1],
s1 = Str(" * ", f[i, 1]);
if (f[i, 2] != 1, s1 = Str(s1, "^", f[i, 2]));
s = Str(s, s1)
);
s
};
n=0;while(n++, print(fnice(n)))
```
## Pascal
{{works with|Free_Pascal}}
```pascal
program CountInFactors(output);
type
TdynArray = array of integer;
function factorize(number: integer): TdynArray;
var
k: integer;
begin
if number = 1 then
begin
setlength(factorize, 1);
factorize[0] := 1
end
else
begin
k := 2;
while number > 1 do
begin
while number mod k = 0 do
begin
setlength(factorize, length(factorize) + 1);
factorize[high(factorize)] := k;
number := number div k;
end;
inc(k);
end;
end
end;
var
i, j: integer;
fac: TdynArray;
begin
for i := 1 to 22 do
begin
write(i, ': ' );
fac := factorize(i);
write(fac[0]);
for j := 1 to high(fac) do
write(' * ', fac[j]);
writeln;
end;
end.
```
{{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
19: 19
20: 2 * 2 * 5
21: 3 * 7
22: 2 * 11
```
## Perl
Typically one would use a module for this. Note that these modules all return an empty list for '1'. This should be efficient to 50+ digits:{{libheader|ntheory}}
```perl
use ntheory qw/factor/;
print "$_ = ", join(" x ", factor($_)), "\n" for 1000000000000000000 .. 1000000000000000010;
```
{{out}}
```txt
1000000000000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
1000000000000000001 = 101 x 9901 x 999999000001
1000000000000000002 = 2 x 3 x 17 x 131 x 1427 x 52445056723
1000000000000000003 = 1000000000000000003
1000000000000000004 = 2 x 2 x 1801 x 246809 x 562425889
1000000000000000005 = 3 x 5 x 44087 x 691381 x 2187161
1000000000000000006 = 2 x 7 x 919 x 77724234416291
1000000000000000007 = 1370531 x 729644203597
1000000000000000008 = 2 x 2 x 2 x 3 x 3 x 97 x 26209 x 32779 x 166667
1000000000000000009 = 1000000000000000009
1000000000000000010 = 2 x 5 x 11 x 103 x 4013 x 21993833369
```
Giving similar output and also good for large inputs:
```perl
use Math::Pari qw/factorint/;
sub factor {
my ($pn,$pc) = @{Math::Pari::factorint(shift)};
return map { ($pn->[$_]) x $pc->[$_] } 0 .. $#$pn;
}
print "$_ = ", join(" x ", factor($_)), "\n" for 1000000000000000000 .. 1000000000000000010;
```
or, somewhat slower and limited to native 32-bit or 64-bit integers only:
```perl
use Math::Factor::XS qw/prime_factors/;
print "$_ = ", join(" x ", prime_factors($_)), "\n" for 1000000000000000000 .. 1000000000000000010;
```
If we want to implement it self-contained, we could use the prime decomposition routine from the [[Prime_decomposition]] task. This is reasonably fast and small, though much slower than the modules and certainly could have more optimization.
```perl
sub factors {
my($n, $p, @out) = (shift, 3);
return if $n < 1;
while (!($n&1)) { $n >>= 1; push @out, 2; }
while ($n > 1 && $p*$p <= $n) {
while ( ($n % $p) == 0) {
$n /= $p;
push @out, $p;
}
$p += 2;
}
push @out, $n if $n > 1;
@out;
}
print "$_ = ", join(" x ", factors($_)), "\n" for 100000000000 .. 100000000100;
```
We could use the second extensible sieve from [[Sieve_of_Eratosthenes#Extensible_sieves]] to only divide by primes.
```perl
tie my @primes, 'Tie::SieveOfEratosthenes';
sub factors {
my($n, $i, $p, @out) = (shift, 0, 2);
while ($n >= $p * $p) {
while ($n % $p == 0) {
push @out, $p;
$n /= $p;
}
$p = $primes[++$i];
}
push @out, $n if $n > 1 || !@out;
@out;
}
print "$_ = ", join(" x ", factors($_)), "\n" for 100000000000 .. 100000000010;
```
{{out}}
```txt
100000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
100000000001 = 11 x 11 x 23 x 4093 x 8779
100000000002 = 2 x 3 x 7 x 1543 x 1543067
100000000003 = 100000000003
100000000004 = 2 x 2 x 17573 x 1422637
100000000005 = 3 x 5 x 19 x 1627 x 215659
100000000006 = 2 x 3947 x 12667849
100000000007 = 353 x 283286119
100000000008 = 2 x 2 x 2 x 3 x 3 x 3 x 462962963
100000000009 = 7 x 13 x 53 x 1979 x 10477
100000000010 = 2 x 5 x 101 x 3541 x 27961
```
This next example isn't quite as fast and uses much more memory, but it is self-contained and shows a different approach. As written it must start at 1, but a range can be handled by using a map to prefill the p_and_sq array.
```perl
#!perl -C
use utf8;
use strict;
use warnings;
my $limit = 1000;
print "$_ = $_\n" for 1..3;
my @p_and_sq = ( [2, 4], [3, 9] );
N: for my $n ( 4 .. 1000 ) {
print $n, " = ";
for( my $i = 0; $i <= $#p_and_sq; ++$i ) {
my ($p, $sq) = @{ $p_and_sq[$i] };
if( $sq > $n ) {
print $n, "\n";
push @p_and_sq, [ $n, $n*$n ];
next N;
}
while( 0 == ($n % $p) ) {
print $p;
$n /= $p;
if( $n == 1 ) {
print "\n";
next N;
}
print " × ";
}
}
die "Ran out of primes?!";
}
```
## Perl 6
{{works with|rakudo|2015-10-01}}
```perl6
constant @primes = 2, |(3, 5, 7 ... *).grep: *.is-prime;
multi factors(1) { 1 }
multi factors(Int $remainder is copy) {
gather for @primes -> $factor {
# if remainder < factor², we're done
if $factor * $factor > $remainder {
take $remainder if $remainder > 1;
last;
}
# How many times can we divide by this prime?
while $remainder %% $factor {
take $factor;
last if ($remainder div= $factor) === 1;
}
}
}
say "$_: ", factors($_).join(" × ") for 1..*;
```
The first twenty numbers:
```txt
1: 1
2: 2
3: 3
4: 2 × 2
5: 5
6: 2 × 3
7: 7
8: 2 × 2 × 2
9: 3 × 3
10: 2 × 5
11: 11
12: 2 × 2 × 3
13: 13
14: 2 × 7
15: 3 × 5
16: 2 × 2 × 2 × 2
17: 17
18: 2 × 3 × 3
19: 19
20: 2 × 2 × 5
```
Here we use a multi declaration with a constant parameter to match the degenerate case. We use copy parameters when we wish to reuse the formal parameter as a mutable variable within the function. (Parameters default to readonly in Perl 6.) Note the use of gather/take as the final statement in the function, which is a common Perl 6 idiom to set up a coroutine within a function to return a lazy list on demand.
Note also the '×' above is not ASCII 'x', but U+00D7 MULTIPLICATION SIGN. Perl 6 does Unicode natively.
Here is a solution inspired from [[Almost_prime#C]]. It doesn't use &is-prime.
```perl6
sub factor($n is copy) {
$n == 1 ?? 1 !!
gather {
$n /= take 2 while $n %% 2;
$n /= take 3 while $n %% 3;
loop (my $p = 5; $p*$p <= $n; $p+=2) {
$n /= take $p while $n %% $p;
}
take $n unless $n == 1;
}
}
say "$_ == ", join " \x00d7 ", factor $_ for 1 .. 20;
```
Same output as above.
Alternately, use a module:
```perl6
use Prime::Factor;
say "$_ = {(.&prime-factors || 1).join: ' x ' }" for flat 1 .. 10, 10**20 .. 10**20 + 10;
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
100000000000000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
100000000000000000001 = 73 x 137 x 1676321 x 5964848081
100000000000000000002 = 2 x 3 x 155977777 x 106852828571
100000000000000000003 = 373 x 155773 x 1721071782307
100000000000000000004 = 2 x 2 x 13 x 1597 x 240841 x 4999900001
100000000000000000005 = 3 x 5 x 7 x 7 x 83 x 1663 x 985694468327
100000000000000000006 = 2 x 31 x 6079 x 265323774602147
100000000000000000007 = 67 x 166909 x 8942221889969
100000000000000000008 = 2 x 2 x 2 x 3 x 3 x 3 x 233 x 1986965506278811
100000000000000000009 = 557 x 72937 x 2461483384901
100000000000000000010 = 2 x 5 x 11 x 909090909090909091
```
## Phix
```Phix
function factorise(atom n)
-- returns a list of all integer factors of n, that when multiplied together equal n
-- (adapted from the standard builtin factors(), which does not return duplicates)
sequence res = {}
integer p = 2,
step = 1,
lim = floor(sqrt(n))
while p<=lim do
while remainder(n,p)=0 do
res = append(res,sprintf("%d",p))
n = n/p
if n=p then exit end if
lim = floor(sqrt(n))
end while
p += step
step = 2
end while
return join(append(res,sprintf("%d",n))," x ")
end function
for i=1 to 10 do
printf(1,"%2d: %s\n",{i,factorise(i)})
end for
```
{{out}}
```txt
1: 1
2: 2
3: 3
4: 2 x 2
5: 5
6: 2 x 3
7: 7
8: 2 x 2 x 2
9: 3 x 3
10: 2 x 5
```
## PicoLisp
This is the 'factor' function from [[Prime decomposition#PicoLisp]].
```PicoLisp
(de factor (N)
(make
(let (D 2 L (1 2 2 . (4 2 4 2 4 6 2 6 .)) M (sqrt N))
(while (>= M D)
(if (=0 (% N D))
(setq M (sqrt (setq N (/ N (link D)))))
(inc 'D (pop 'L)) ) )
(link N) ) ) )
(for N 20
(prinl N ": " (glue " * " (factor N))) )
```
{{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
19: 19
20: 2 * 2 * 5
```
## PL/I
```PL/I
cnt: procedure options (main);
declare (i, k, n) fixed binary;
declare first bit (1) aligned;
do n = 1 to 40;
put skip list (n || ' =');
k = n; first = '1'b;
repeat:
do i = 2 to k-1;
if mod(k, i) = 0 then
do;
k = k/i;
if ^first then put edit (' x ')(A);
first = '0'b;
put edit (trim(i)) (A);
go to repeat;
end;
end;
if ^first then put edit (' x ')(A);
if n = 1 then i = 1;
put edit (trim(i)) (A);
end;
end cnt;
```
Results:
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17 = 17
18 = 2 x 3 x 3
19 = 19
20 = 2 x 2 x 5
21 = 3 x 7
22 = 2 x 11
23 = 23
24 = 2 x 2 x 2 x 3
25 = 5 x 5
26 = 2 x 13
27 = 3 x 3 x 3
28 = 2 x 2 x 7
29 = 29
30 = 2 x 3 x 5
31 = 31
32 = 2 x 2 x 2 x 2 x 2
33 = 3 x 11
34 = 2 x 17
35 = 5 x 7
36 = 2 x 2 x 3 x 3
37 = 37
38 = 2 x 19
39 = 3 x 13
40 = 2 x 2 x 2 x 5
```
## PowerShell
```PowerShell
function eratosthenes ($n) {
if($n -ge 1){
$prime = @(1..($n+1) | foreach{$true})
$prime[1] = $false
$m = [Math]::Floor([Math]::Sqrt($n))
for($i = 2; $i -le $m; $i++) {
if($prime[$i]) {
for($j = $i*$i; $j -le $n; $j += $i) {
$prime[$j] = $false
}
}
}
1..$n | where{$prime[$_]}
} else {
"$n must be equal or greater than 1"
}
}
function prime-decomposition ($n) {
$array = eratosthenes $n
$prime = @()
foreach($p in $array) {
while($n%$p -eq 0) {
$n /= $p
$prime += @($p)
}
}
$prime
}
$OFS = " x "
"$(prime-decomposition 2144)"
"$(prime-decomposition 100)"
"$(prime-decomposition 12)"
```
Output:
```txt
2 x 2 x 2 x 2 x 2 x 67
2 x 2 x 5 x 5
2 x 2 x 3
```
## PureBasic
```PureBasic
Procedure Factorize(Number, List Factors())
Protected I = 3, Max
ClearList(Factors())
While Number % 2 = 0
AddElement(Factors())
Factors() = 2
Number / 2
Wend
Max = Number
While I <= Max And Number > 1
While Number % I = 0
AddElement(Factors())
Factors() = I
Number / I
Wend
I + 2
Wend
EndProcedure
If OpenConsole()
NewList n()
For a=1 To 20
text$=RSet(Str(a),2)+"= "
Factorize(a,n())
If ListSize(n())
ResetList(n())
While NextElement(n())
text$ + Str(n())
If ListSize(n())-ListIndex(n())>1
text$ + "*"
EndIf
Wend
Else
text$+Str(a) ; To handle the '1', which is not really a prime...
EndIf
PrintN(text$)
Next a
EndIf
```
{{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
19= 19
20= 2*2*5
```
## Python
This uses the [http://docs.python.org/dev/library/functools.html#functools.lru_cache functools.lru_cache] standard library module to cache intermediate results.
```python
from functools import lru_cache
primes = [2, 3, 5, 7, 11, 13, 17] # Will be extended
@lru_cache(maxsize=2000)
def pfactor(n):
if n == 1:
return [1]
n2 = n // 2 + 1
for p in primes:
if p <= n2:
d, m = divmod(n, p)
if m == 0:
if d > 1:
return [p] + pfactor(d)
else:
return [p]
else:
if n > primes[-1]:
primes.append(n)
return [n]
if __name__ == '__main__':
mx = 5000
for n in range(1, mx + 1):
factors = pfactor(n)
if n <= 10 or n >= mx - 20:
print( '%4i %5s %s' % (n,
'' if factors != [n] or n == 1 else 'prime',
'x'.join(str(i) for i in factors)) )
if n == 11:
print('...')
print('\nNumber of primes gathered up to', n, 'is', len(primes))
print(pfactor.cache_info())
```
{{out}}
```txt
1 1
2 prime 2
3 prime 3
4 2x2
5 prime 5
6 2x3
7 prime 7
8 2x2x2
9 3x3
10 2x5
...
4980 2x2x3x5x83
4981 17x293
4982 2x47x53
4983 3x11x151
4984 2x2x2x7x89
4985 5x997
4986 2x3x3x277
4987 prime 4987
4988 2x2x29x43
4989 3x1663
4990 2x5x499
4991 7x23x31
4992 2x2x2x2x2x2x2x3x13
4993 prime 4993
4994 2x11x227
4995 3x3x3x5x37
4996 2x2x1249
4997 19x263
4998 2x3x7x7x17
4999 prime 4999
5000 2x2x2x5x5x5x5
Number of primes gathered up to 5000 is 669
CacheInfo(hits=3935, misses=7930, maxsize=2000, currsize=2000)
```
## R
```R
#initially I created a function which returns prime factors then I have created another function counts in the factors and #prints the values.
findfactors <- function(num) {
x <- c()
p1<- 2
p2 <- 3
everyprime <- num
while( everyprime != 1 ) {
while( everyprime%%p1 == 0 ) {
x <- c(x, p1)
everyprime <- floor(everyprime/ p1)
}
p1 <- p2
p2 <- p2 + 2
}
x
}
count_in_factors=function(x){
primes=findfactors(x)
x=c(1)
for (i in 1:length(primes)) {
x=paste(primes[i],"x",x)
}
return(x)
}
count_in_factors(72)
```
{{out}}
```txt
[1] "3 x 3 x 2 x 2 x 2 x 1"
```
## Racket
See also [[#Scheme]]. This uses Racket’s math/number-theory package
```racket
#lang typed/racket
(require math/number-theory)
(define (factorise-as-primes [n : Natural])
(if
(= n 1)
'(1)
(let ((F (factorize n)))
(append*
(for/list : (Listof (Listof Natural))
((f (in-list F)))
(make-list (second f) (first f)))))))
(define (factor-count [start-inc : Natural] [end-inc : Natural])
(for ((i : Natural (in-range start-inc (add1 end-inc))))
(define f (string-join (map number->string (factorise-as-primes i)) " × "))
(printf "~a:\t~a~%" i f)))
(factor-count 1 22)
(factor-count 2140 2150)
; tb
```
{{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
19: 19
20: 2 × 2 × 5
21: 3 × 7
22: 2 × 11
2140: 2 × 2 × 5 × 107
2141: 2141
2142: 2 × 3 × 3 × 7 × 17
2143: 2143
2144: 2 × 2 × 2 × 2 × 2 × 67
2145: 3 × 5 × 11 × 13
2146: 2 × 29 × 37
2147: 19 × 113
2148: 2 × 2 × 3 × 179
2149: 7 × 307
2150: 2 × 5 × 5 × 43
```
## REXX
### simple approach
As per the task's requirements, the prime factors of '''1''' (unity) will be listed as '''1''',
even though, strictly speaking, it should be '''null'''. The same applies to '''0'''.
Programming note: if the '''high''' argument is negative, its positive value is used and no displaying of the
prime factors are listed, but the number of primes found is always shown. The showing of the count of
primes was included to help verify the factoring (of composites).
```rexx
/*REXX program lists the prime factors of a specified integer (or a range of integers).*/
@.=left('', 8); @.0="{unity} "; @.1='[prime] ' /*some tags and handy-dandy literals.*/
parse arg LO HI @ . /*get optional arguments from the C.L. */
if LO=='' | LO=="," then do; LO=1; HI=40; end /*Not specified? Then use the default.*/
if HI=='' | HI=="," then HI= LO /* " " " " " " */
if @=='' then @= 'x' /* " " " " " " */
if length(@)\==1 then @= x2c(@) /*Not length 1? Then use hexadecimal. */
tell= (HI>0) /*if HIGH is positive, then show #'s.*/
HI= abs(HI) /*use the absolute value for HIGH. */
w= length(HI) /*get maximum width for pretty output. */
numeric digits max(9, w + 1) /*maybe bump the precision of numbers. */
#= 0 /*the number of primes found (so far). */
do n=abs(LO) to HI; f= factr(n) /*process a single number or a range.*/
p= words( translate(f, ,@) ) - (n==1) /*P: is the number of prime factors. */
if p==1 then #= # + 1 /*bump the primes counter (exclude N=1)*/
if tell then say right(n, w) '=' @.p f /*display if a prime, plus its factors.*/
end /*n*/
say
say right(#, w) ' primes found.' /*display the number of primes found. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: procedure expose @; parse arg z 1 n,$; if z<2 then return z /*is Z too small?*/
do while z//2==0; $= $||@||2; z= z%2; end /*maybe add factor of 2 */
do while z//3==0; $= $||@||3; z= z%3; end /* " " " " 3 */
do while z//5==0; $= $||@||5; z= z%5; end /* " " " " 5 */
do while z//7==0; $= $||@||7; z= z%7; end /* " " " " 7 */
do j=11 by 6 while j<=z /*insure that J isn't divisible by 3.*/
parse var j '' -1 _ /*get the last decimal digit of J. */
if _\==5 then do while z//j==0; $=$||@||j; z= z%j; end /*maybe reduce Z.*/
if _ ==3 then iterate /*Next # ÷ by 5? Skip. ___ */
if j*j>n then leave /*are we higher than the √ N ? */
y= j + 2 /*obtain the next odd divisor. */
do while z//y==0; $=$||@||y; z= z%y; end /*maybe reduce Z.*/
end /*j*/
if z==1 then return substr($, 1+length(@) ) /*Is residual=1? Don't add 1*/
return substr($||@||z, 1+length(@) ) /*elide superfluous header. */
```
{{out|output|text= when using the default inputs:}}
```txt
1 = {unity} 1
2 = [prime] 2
3 = [prime] 3
4 = 2x2
5 = [prime] 5
6 = 2x3
7 = [prime] 7
8 = 2x2x2
9 = 3x3
10 = 2x5
11 = [prime] 11
12 = 2x2x3
13 = [prime] 13
14 = 2x7
15 = 3x5
16 = 2x2x2x2
17 = [prime] 17
18 = 2x3x3
19 = [prime] 19
20 = 2x2x5
21 = 3x7
22 = 2x11
23 = [prime] 23
24 = 2x2x2x3
25 = 5x5
26 = 2x13
27 = 3x3x3
28 = 2x2x7
29 = [prime] 29
30 = 2x3x5
31 = [prime] 31
32 = 2x2x2x2x2
33 = 3x11
34 = 2x17
35 = 5x7
36 = 2x2x3x3
37 = [prime] 37
38 = 2x19
39 = 3x13
40 = 2x2x2x5
12 primes found.
```
{{out|output|text= when the following input was used: 1 12 207820
```txt
1 = {unity} 1
2 = [prime] 2
3 = [prime] 3
4 = 2 x 2
5 = [prime] 5
6 = 2 x 3
7 = [prime] 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = [prime] 11
12 = 2 x 2 x 3
5 primes found.
```
{{out|output|text= when the following input was used: 1 -10000
```txt
1229 primes found.
```
{{out|output|text= when the following input was used: 1 -100000
```txt
9592 primes found.
```
### using integer SQRT
This REXX version computes the ''integer square root'' of the integer being factor (to limit the range of factors),
this makes this version about '''50%''' faster than the 1st REXX version.
Also, the number of early testing of prime factors was expanded.
Note that the '''integer square root''' section of code doesn't use any floating point numbers, just integers.
```rexx
/*REXX program lists the prime factors of a specified integer (or a range of integers).*/
@.=left('', 8); @.0="{unity} "; @.1='[prime] ' /*some tags and handy-dandy literals.*/
parse arg LO HI @ . /*get optional arguments from the C.L. */
if LO=='' | LO=="," then do; LO=1; HI=40; end /*Not specified? Then use the default.*/
if HI=='' | HI=="," then HI= LO /* " " " " " " */
if @=='' then @= 'x' /* " " " " " " */
if length(@)\==1 then @= x2c(@) /*Not length 1? Then use hexadecimal. */
tell= (HI>0) /*if HIGH is positive, then show #'s.*/
HI= abs(HI) /*use the absolute value for HIGH. */
w= length(HI) /*get maximum width for pretty output. */
numeric digits max(9, w + 1) /*maybe bump the precision of numbers. */
#= 0 /*the number of primes found (so far). */
do n=abs(LO) to HI; f= factr(n) /*process a single number or a range.*/
p= words( translate(f, ,@) ) - (n==1) /*P: is the number of prime factors. */
if p==1 then #= # + 1 /*bump the primes counter (exclude N=1)*/
if tell then say right(n, w) '=' @.p f /*display if a prime, plus its factors.*/
end /*n*/
say
say right(#, w) ' primes found.' /*display the number of primes found. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: procedure expose @; parse arg z 1 n,$; if z<2 then return z /*is Z too small?*/
do while z// 2==0; $= $||@||2 ; z= z%2 ; end /*maybe add factor of 2 */
do while z// 3==0; $= $||@||3 ; z= z%3 ; end /* " " " " 3 */
do while z// 5==0; $= $||@||5 ; z= z%5 ; end /* " " " " 5 */
do while z// 7==0; $= $||@||7 ; z= z%7 ; end /* " " " " 7 */
do while z//11==0; $= $||@||11; z= z%11; end /* " " " " 11 */
do while z//13==0; $= $||@||13; z= z%13; end /* " " " " 13 */
do while z//17==0; $= $||@||17; z= z%17; end /* " " " " 17 */
do while z//19==0; $= $||@||19; z= z%19; end /* " " " " 19 */
do while z//23==0; $= $||@||23; z= z%23; end /* " " " " 23 */
do while z//29==0; $= $||@||29; z= z%29; end /* " " " " 29 */
do while z//31==0; $= $||@||31; z= z%31; end /* " " " " 31 */
do while z//37==0; $= $||@||37; z= z%37; end /* " " " " 37 */
if z>40 then do; t= z; q= 1; r= 0; do while q<=t; q= q * 4
end /*while*/
do while q>1; q=q%4; _=t-r-q; r=r%2; if _>=0 then do; t=_; r=r+q
end
end /*while*/ /* [↑] find integer SQRT(z). */
/*R: is the integer SQRT of Z.*/
do j=41 by 6 to r while j<=z /*insure J isn't divisible by 3*/
parse var j '' -1 _ /*get last decimal digit of J.*/
if _\==5 then do while z//j==0; $=$||@||j; z= z%j; end
if _ ==3 then iterate /*Next number ÷ by 5 ? Skip.*/
y= j + 2 /*use the next (odd) divisor. */
do while z//y==0; $=$||@||y; z= z%y; end
end /*j*/ /* [↑] reduce Z by Y ? */
end /*if z>40*/
if z==1 then return substr($, 1+length(@) ) /*Is residual=1? Don't add 1*/
return substr($||@||z, 1+length(@) ) /*elide superfluous header. */
```
{{out|output|text= when using the default inputs:}}
```txt
1 = {unity} 1
2 = [prime] 2
3 = [prime] 3
4 = 2∙2
5 = [prime] 5
6 = 2∙3
7 = [prime] 7
8 = 2∙2∙2
9 = 3∙3
10 = 2∙5
11 = [prime] 11
12 = 2∙2∙3
13 = [prime] 13
14 = 2∙7
15 = 3∙5
16 = 2∙2∙2∙2
17 = [prime] 17
18 = 2∙3∙3
19 = [prime] 19
20 = 2∙2∙5
21 = 3∙7
22 = 2∙11
23 = [prime] 23
24 = 2∙2∙2∙3
25 = 5∙5
26 = 2∙13
27 = 3∙3∙3
28 = 2∙2∙7
29 = [prime] 29
30 = 2∙3∙5
31 = [prime] 31
32 = 2∙2∙2∙2∙2
33 = 3∙11
34 = 2∙17
35 = 5∙7
36 = 2∙2∙3∙3
37 = [prime] 37
38 = 2∙19
39 = 3∙13
40 = 2∙2∙2∙5
12 primes found.
```
## Ring
```ring
for i = 1 to 20
see "" + i + " = " + factors(i) + nl
next
func factors n
f = ""
if n = 1 return "1" ok
p = 2
while p <= n
if (n % p) = 0
f += string(p) + " x "
n = n/p
else p += 1 ok
end
return left(f, len(f) - 3)
```
Output:
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3
13 = 13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17 = 17
18 = 2 x 3 x 3
19 = 19
20 = 2 x 2 x 5
```
## Ruby
Starting with Ruby 1.9, 'prime' is part of the standard library and provides Integer#prime_division.
```ruby
require 'optparse'
require 'prime'
maximum = 10
OptionParser.new do |o|
o.banner = "Usage: #{File.basename $0} [-m MAXIMUM]"
o.on("-m MAXIMUM", Integer,
"Count up to MAXIMUM [#{maximum}]") { |m| maximum = m }
o.parse! rescue ($stderr.puts $!, o; exit 1)
($stderr.puts o; exit 1) unless ARGV.size == 0
end
# 1 has no prime factors
puts "1 is 1" unless maximum < 1
2.upto(maximum) do |i|
# i is 504 => i.prime_division is [[2, 3], [3, 2], [7, 1]]
f = i.prime_division.map! do |factor, exponent|
# convert [2, 3] to "2 x 2 x 2"
([factor] * exponent).join " x "
end.join " x "
puts "#{i} is #{f}"
end
```
{{out|Example}}
```txt
$ ruby prime-count.rb -h
Usage: prime-count.rb [-m MAXIMUM]
-m MAXIMUM Count up to MAXIMUM [10]
$ ruby prime-count.rb -m 10000 | sed -e '11,9990d'
1 is 1
2 is 2
3 is 3
4 is 2 x 2
5 is 5
6 is 2 x 3
7 is 7
8 is 2 x 2 x 2
9 is 3 x 3
10 is 2 x 5
9991 is 97 x 103
9992 is 2 x 2 x 2 x 1249
9993 is 3 x 3331
9994 is 2 x 19 x 263
9995 is 5 x 1999
9996 is 2 x 2 x 3 x 7 x 7 x 17
9997 is 13 x 769
9998 is 2 x 4999
9999 is 3 x 3 x 11 x 101
10000 is 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
```
## Run BASIC
```runbasic
for i = 1000 to 1016
print i;" = "; factorial$(i)
next
wait
function factorial$(num)
if num = 1 then factorial$ = "1"
fct = 2
while fct <= num
if (num mod fct) = 0 then
factorial$ = factorial$ ; x$ ; fct
x$ = " x "
num = num / fct
else
fct = fct + 1
end if
wend
end function
```
{{out}}
```txt
1000 = 2 x 2 x 2 x 5 x 5 x 5
1001 = 7 x 11 x 13
1002 = 2 x 3 x 167
1003 = 17 x 59
1004 = 2 x 2 x 251
1005 = 3 x 5 x 67
1006 = 2 x 503
1007 = 19 x 53
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
1009 = 1009
1010 = 2 x 5 x 101
1011 = 3 x 337
1012 = 2 x 2 x 11 x 23
1013 = 1013
1014 = 2 x 3 x 13 x 13
1015 = 5 x 7 x 29
1016 = 2 x 2 x 2 x 127
```
## Rust
You can run and experiment with this code at https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=b66c14d944ff0472d2460796513929e2
```rust
use std::env;
fn main() {
let args: Vec<_> = env::args().collect();
let n = if args.len() > 1 {
args[1].parse().expect("Not a valid number to count to")
}
else {
20
};
count_in_factors_to(n);
}
fn count_in_factors_to(n: u64) {
println!("1");
let mut primes = vec![];
for i in 2..=n {
let fs = factors(&primes, i);
if fs.len() <= 1 {
primes.push(i);
println!("{}", i);
}
else {
println!("{} = {}", i, fs.iter().map(|f| f.to_string()).collect::>().join(" x "));
}
}
}
fn factors(primes: &[u64], mut n: u64) -> Vec {
let mut result = Vec::new();
for p in primes {
while n % p == 0 {
result.push(*p);
n /= p;
}
if n == 1 {
return result;
}
}
vec![n]
}
```
{{out}}
```txt
1
2
3
4 = 2 x 2
5
6 = 2 x 3
7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11
12 = 2 x 2 x 3
13
14 = 2 x 7
15 = 3 x 5
16 = 2 x 2 x 2 x 2
17
18 = 2 x 3 x 3
19
20 = 2 x 2 x 5
```
## Scala
```scala
def primeFactors( n:Int ) = {
def primeStream(s: Stream[Int]): Stream[Int] = {
s.head #:: primeStream(s.tail filter { _ % s.head != 0 })
}
val primes = primeStream(Stream.from(2))
def factors( n:Int ) : List[Int] = primes.takeWhile( _ <= n ).find( n % _ == 0 ) match {
case None => Nil
case Some(p) => p :: factors( n/p )
}
if( n == 1 ) List(1) else factors(n)
}
// A little test...
{
val nums = (1 to 12).toList :+ 2144 :+ 6358
nums.foreach( n => println( "%6d : %s".format( n, primeFactors(n).mkString(" * ") ) ) )
}
```
{{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
2144 : 2 * 2 * 2 * 2 * 2 * 67
6358 : 2 * 11 * 17 * 17
```
## Scheme
```lisp
(define (factors n)
(let facs ((l '()) (d 2) (x n))
(cond ((= x 1) (if (null? l) '(1) l))
((< x (* d d)) (cons x l))
(else (if (= 0 (modulo x d))
(facs (cons d l) d (/ x d))
(facs l (+ 1 d) x))))))
(define (show l)
(display (car l))
(if (not (null? (cdr l)))
(begin
(display " × ")
(show (cdr l)))
(display "\n")))
(do ((i 1 (+ i 1))) (#f)
(display i)
(display " = ")
(show (reverse (factors i))))
```
{{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
...
```
## Seed7
```seed7
$ include "seed7_05.s7i";
const proc: writePrimeFactors (in var integer: number) is func
local
var boolean: laterElement is FALSE;
var integer: checker is 2;
begin
while checker * checker <= number do
if number rem checker = 0 then
if laterElement then
write(" * ");
end if;
laterElement := TRUE;
write(checker);
number := number div checker;
else
incr(checker);
end if;
end while;
if number <> 1 then
if laterElement then
write(" * ");
end if;
laterElement := TRUE;
write(number);
end if;
end func;
const proc: main is func
local
var integer: number is 0;
begin
writeln("1: 1");
for number range 2 to 2147483647 do
write(number <& ": ");
writePrimeFactors(number);
writeln;
end for;
end func;
```
{{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
. . .
```
## Sidef
```ruby
class Counter {
method factors(n, p=2) {
var a = gather {
while (n >= p*p) {
while (p `divides` n) {
take(p)
n //= p
}
p = self.next_prime(p)
}
}
(n > 1 || a.is_empty) ? (a << n) : a
}
method is_prime(n) {
self.factors(n).len == 1
}
method next_prime(p) {
do {
p == 2 ? (p = 3) : (p+=2)
} while (!self.is_prime(p))
return p
}
}
for i in (1..100) {
say "#{i} = #{Counter().factors(i).join(' × ')}"
}
```
## Tcl
This factorization code is based on the same engine that is used in the [[Parallel calculations#Tcl|parallel computation task]].
```tcl
package require Tcl 8.5
namespace eval prime {
variable primes [list 2 3 5 7 11]
proc restart {} {
variable index -1
variable primes
variable current [lindex $primes end]
}
proc get_next_prime {} {
variable primes
variable index
if {$index < [llength $primes]-1} {
return [lindex $primes [incr index]]
}
variable current
while 1 {
incr current 2
set p 1
foreach prime $primes {
if {$current % $prime} {} else {
set p 0
break
}
}
if {$p} {
return [lindex [lappend primes $current] [incr index]]
}
}
}
proc factors {num} {
restart
set factors [dict create]
for {set i [get_next_prime]} {$i <= $num} {} {
if {$num % $i == 0} {
dict incr factors $i
set num [expr {$num / $i}]
continue
} elseif {$i*$i > $num} {
dict incr factors $num
break
} else {
set i [get_next_prime]
}
}
return $factors
}
# Produce the factors in rendered form
proc factors.rendered {num} {
set factorDict [factors $num]
if {[dict size $factorDict] == 0} {
return 1
}
dict for {factor times} $factorDict {
lappend v {*}[lrepeat $times $factor]
}
return [join $v "*"]
}
}
```
Demonstration code:
```tcl
set max 20
for {set i 1} {$i <= $max} {incr i} {
puts [format "%*d = %s" [string length $max] $i [prime::factors.rendered $i]]
}
```
## VBScript
Made minor modifications on the code I posted under Prime Decomposition.
```vb
Function CountFactors(n)
If n = 1 Then
CountFactors = 1
Else
arrP = Split(ListPrimes(n)," ")
Set arrList = CreateObject("System.Collections.ArrayList")
divnum = n
Do Until divnum = 1
'The -1 is to account for the null element of arrP
For i = 0 To UBound(arrP)-1
If divnum = 1 Then
Exit For
ElseIf divnum Mod arrP(i) = 0 Then
divnum = divnum/arrP(i)
arrList.Add arrP(i)
End If
Next
Loop
arrList.Sort
For i = 0 To arrList.Count - 1
If i = arrList.Count - 1 Then
CountFactors = CountFactors & arrList(i)
Else
CountFactors = CountFactors & arrList(i) & " * "
End If
Next
End If
End Function
Function IsPrime(n)
If n = 2 Then
IsPrime = True
ElseIf n <= 1 Or n Mod 2 = 0 Then
IsPrime = False
Else
IsPrime = True
For i = 3 To Int(Sqr(n)) Step 2
If n Mod i = 0 Then
IsPrime = False
Exit For
End If
Next
End If
End Function
Function ListPrimes(n)
ListPrimes = ""
For i = 1 To n
If IsPrime(i) Then
ListPrimes = ListPrimes & i & " "
End If
Next
End Function
'Testing the fucntions.
WScript.StdOut.Write "2 = " & CountFactors(2)
WScript.StdOut.WriteLine
WScript.StdOut.Write "2144 = " & CountFactors(2144)
WScript.StdOut.WriteLine
```
{{Out}}
```txt
2 = 2
2144 = 2 * 2 * 2 * 2 * 2 * 67
```
## Visual Basic .NET
```vbnet
Module CountingInFactors
Sub Main()
For i As Integer = 1 To 10
Console.WriteLine("{0} = {1}", i, CountingInFactors(i))
Next
For i As Integer = 9991 To 10000
Console.WriteLine("{0} = {1}", i, CountingInFactors(i))
Next
End Sub
Private Function CountingInFactors(ByVal n As Integer) As String
If n = 1 Then Return "1"
Dim sb As New Text.StringBuilder()
CheckFactor(2, n, sb)
If n = 1 Then Return sb.ToString()
CheckFactor(3, n, sb)
If n = 1 Then Return sb.ToString()
For i As Integer = 5 To n Step 2
If i Mod 3 = 0 Then Continue For
CheckFactor(i, n, sb)
If n = 1 Then Exit For
Next
Return sb.ToString()
End Function
Private Sub CheckFactor(ByVal mult As Integer, ByRef n As Integer, ByRef sb As Text.StringBuilder)
Do While n Mod mult = 0
If sb.Length > 0 Then sb.Append(" x ")
sb.Append(mult)
n = n / mult
Loop
End Sub
End Module
```
{{out}}
```txt
1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
9991 = 97 x 103
9992 = 2 x 2 x 2 x 1249
9993 = 3 x 3331
9994 = 2 x 19 x 263
9995 = 5 x 1999
9996 = 2 x 2 x 3 x 7 x 7 x 17
9997 = 13 x 769
9998 = 2 x 4999
9999 = 3 x 3 x 11 x 101
10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
```
## 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;
]
```
Example output:
```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
```zkl
foreach n in ([1..*]){ println(n,": ",primeFactors(n).concat("\U2715;")) }
```
Using the fixed size integer (64 bit) solution from [[Prime decomposition#zkl]]
```zkl
fcn primeFactors(n){ // Return a list of factors of n
acc:=fcn(n,k,acc,maxD){ // k is 2,3,5,7,9,... not optimum
if(n==1 or k>maxD) acc.close();
else{
q,r:=n.divr(k); // divr-->(quotient,remainder)
if(r==0) return(self.fcn(q,k,acc.write(k),q.toFloat().sqrt()));
return(self.fcn(n,k+1+k.isOdd,acc,maxD))
}
}(n,2,Sink(List),n.toFloat().sqrt());
m:=acc.reduce('*,1); // mulitply factors
if(n!=m) acc.append(n/m); // opps, missed last factor
else acc;
}
```
{{out}}
```txt
1:
2: 2
3: 3
4: 2✕2
5: 5
6: 2✕3
...
591885: 3✕3✕5✕7✕1879
591886: 2✕295943
591887: 591887
591888: 2✕2✕2✕2✕3✕11✕19✕59
...
```
## ZX Spectrum Basic
{{trans|BBC_BASIC}}
```zxbasic
10 FOR i=1 TO 20
20 PRINT i;" = ";
30 IF i=1 THEN PRINT 1: GO TO 90
40 LET p=2: LET n=i: LET f$=""
50 IF p>n THEN GO TO 80
60 IF NOT FN m(n,p) THEN LET f$=f$+STR$ p+" x ": LET n=INT (n/p): GO TO 50
70 LET p=p+1: GO TO 50
80 PRINT f$( TO LEN f$-3)
90 NEXT i
100 STOP
110 DEF FN m(a,b)=a-INT (a/b)*b
```