# Count in factors

Count in factors
You are encouraged to solve this task according to the task description, using any language you may know.

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   ${\displaystyle 2\times 3}$.
2144   is not prime;   it would be shown as   ${\displaystyle 2\times 2\times 2\times 2\times 2\times 67}$.

## 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
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
Output:
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

The solution uses the generic package Prime_Numbers from Prime decomposition#Ada

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
if Index /= List'Last then
end if;
end loop;
end Put;

N  : Natural := 1;
Max_N : Natural := 15; -- the default for Max_N
begin
end if; -- else use the default
loop
Ada.Text_IO.Put (Integer'Image (N) & ": ");
Put (Decompose (N));
N := N + 1;
exit when N > Max_N;
end loop;
end Count;
Output:
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

Translation of: Euphoria
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
Output:
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

Translation of: D
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
Output:
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

# 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:

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

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:

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).

1>>>>:.48*"=",,::1-#v_.v
$<<<^[email protected]#-"e":+1,+55$2<<<
v4_^#-1:/.:g00_00g1+>>0v
>8*"x",,:00g%!^!%g00:p0<
Output:
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.

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

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;
}
Output:
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++

#include <iostream>
#include <sstream>
#include <iomanip>
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" );
}

Output:
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#

using System;
using System.Collections.Generic;

namespace prog
{
class MainClass
{
public static void Main (string[] args)
{
for( int i=1; i<=22; i++ )
{
List<int> f = Factorize(i);
Console.Write( i + ": " + f[0] );
for( int j=1; j<f.Count; j++ )
{
Console.Write( " * " + f[j] );
}
Console.WriteLine();
}
}

public static List<int> Factorize( int n )
{
List<int> l = new List<int>();

if ( n == 1 )
{
}
else
{
int k = 2;
while( n > 1 )
{
while( n % k == 0 )
{
n /= k;
}
k++;
}
}
return l;
}
}
}

## Clojure

(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:
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

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:

(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))))
Output:
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):

(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

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());
}
Output:
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

Library: 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 ).
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;

$close /nolog primes$ 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
Output:
$@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 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)); Output: 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 (define (task (nfrom 2) (range 20)) (for ((i (in-range nfrom (+ nfrom range)))) (writeln i "=" (string-join (prime-factors i) " x ")))) Output: (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 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: 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 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) Output: 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 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
Output:
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

## F#

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)))
Output:
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
:

## 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.

!-*- 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

' 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
Output:
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.

i = 1
while true
{
println[join[" x ", factorFlat[i]]]
i = i + 1
}

## 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()
}
}
Output:
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

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 ')}"
}
Output:
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

Using factorize function from the prime decomposition task,

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

Output:
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.

## Icon and Unicon

procedure main()
write("Press ^C to terminate")
every f := [i:= 1] | factors(i := seq(2)) do {
writes(i," : [")
every writes(" ",!f|"]\n")
}
end

Output:
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 ]
...

## J

Solution:Use J's factoring primitive,
q:
Example (including formatting):
('1 : 1',":&> ,"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

Translation of: Visual Basic .NET
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;
}
}
Output:
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

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;
}
Output:
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

function factor_print{T<:Integer}(n::T)
const SEP = " \u00d7 "
-2 < n || return "-1"*SEP*factor_print(-n)
if isprime(n) || n < 2
return string(n)
end
a = T[]
for (k, v) in factor(n)
append!(a, k*ones(T, v))
end
sort!(a)
join(a, SEP)
end

lo = -4
hi = 40
println("Factor print ", lo, " to ", hi)
for i in lo:hi
println(@sprintf("%5d = ", i), factor_print(i))
end

I wrote this solution's factor_print function with ease rather than efficiency in mind. It may be more efficient to first sort the keys of the factor dictionary and to build the string in place, but I find the logic of the presented solution to be clearer. The factor built-in is relevant to this solution only for integers greater than 1, but I've constructed factor_print to return meaningful results for any representable proper integer.

Output:
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

// 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<Int> {
val factors = mutableListOf<Int>()
if (n < 1) return factors
if (n == 1 || isPrime(n)) {
return factors
}
var factor = 2
var nn = n
while (true) {
if (nn % factor == 0) {
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<String>) {
val list = (MutableList(22) { it + 1 } + 2144) + 6358
for (i in list)
println("${"%4d".format(i)} =${getPrimeFactors(i).joinToString(" * ")}")
}
Output:
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

'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
$./count.opt 1 = 1 2 = 2 3 = 3 4 = 2 x 2 5 = 5 6 = 2 x 3 7 = 7 8 = 2 x 2 x 2 ... 6351 = 3 x 29 x 73 6352 = 2 x 2 x 2 x 2 x 397 6353 = 6353 6354 = 2 x 3 x 3 x 353 6355 = 5 x 31 x 41 6356 = 2 x 2 x 7 x 227 6357 = 3 x 13 x 163 6358 = 2 x 11 x 17 x 17 6359 = 6359 ^C ## Octave Octave's factor function returns an array: for (n = 1:20) printf ("%i: ", n) printf ("%i ", factor (n)) printf ("\n") endfor Output: 1: 1 2: 2 3: 3 4: 2 2 5: 5 6: 2 3 7: 7 8: 2 2 2 9: 3 3 10: 2 5 11: 11 12: 2 2 3 13: 13 14: 2 7 15: 3 5 16: 2 2 2 2 17: 17 18: 2 3 3 19: 19 20: 2 2 5 ## PARI/GP fnice(n)={ my(f,s="",s1); if (n < 2, return(n)); f = factor(n); s = Str(s, f[1,1]); if (f[1, 2] != 1, s=Str(s, "^", f[1,2])); for(i=2,#f[,1], s1 = Str(" * ", f[i, 1]); if (f[i, 2] != 1, s1 = Str(s1, "^", f[i, 2])); s = Str(s, s1) ); s }; n=0;while(n++, print(fnice(n))) ## Pascal Works with: Free_Pascal program CountInFactors(output); type TdynArray = array of integer; function factorize(number: integer): TdynArray; var k: integer; begin if number = 1 then begin setlength(factorize, 1); factorize[0] := 1 end else begin k := 2; while number > 1 do begin while number mod k = 0 do begin setlength(factorize, length(factorize) + 1); factorize[high(factorize)] := k; number := number div k; end; inc(k); end; end end; var i, j: integer; fac: TdynArray; begin for i := 1 to 22 do begin write(i, ': ' ); fac := factorize(i); write(fac[0]); for j := 1 to high(fac) do write(' * ', fac[j]); writeln; end; end. Output: 1: 1 2: 2 3: 3 4: 2 * 2 5: 5 6: 2 * 3 7: 7 8: 2 * 2 * 2 9: 3 * 3 10: 2 * 5 11: 11 12: 2 * 2 * 3 13: 13 14: 2 * 7 15: 3 * 5 16: 2 * 2 * 2 * 2 17: 17 18: 2 * 3 * 3 19: 19 20: 2 * 2 * 5 21: 3 * 7 22: 2 * 11 ## Perl Typically one would use a module for this. Note that these modules all return an empty list for '1'. This should be efficient to 50+ digits: use ntheory qw/factor/; print "$_ = ", join(" x ", factor($_)), "\n" for 1000000000000000000 .. 1000000000000000010; Output: 1000000000000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 1000000000000000001 = 101 x 9901 x 999999000001 1000000000000000002 = 2 x 3 x 17 x 131 x 1427 x 52445056723 1000000000000000003 = 1000000000000000003 1000000000000000004 = 2 x 2 x 1801 x 246809 x 562425889 1000000000000000005 = 3 x 5 x 44087 x 691381 x 2187161 1000000000000000006 = 2 x 7 x 919 x 77724234416291 1000000000000000007 = 1370531 x 729644203597 1000000000000000008 = 2 x 2 x 2 x 3 x 3 x 97 x 26209 x 32779 x 166667 1000000000000000009 = 1000000000000000009 1000000000000000010 = 2 x 5 x 11 x 103 x 4013 x 21993833369 Giving similar output and also good for large inputs: use Math::Pari qw/factorint/; sub factor { my ($pn,$pc) = @{Math::Pari::factorint(shift)}; return map { ($pn->[$_]) x$pc->[$_] } 0 ..$#$pn; } print "$_ = ", join(" x ", factor($_)), "\n" for 1000000000000000000 .. 1000000000000000010; or, somewhat slower and limited to native 32-bit or 64-bit integers only: use Math::Factor::XS qw/prime_factors/; print "$_ = ", join(" x ", prime_factors($_)), "\n" for 1000000000000000000 .. 1000000000000000010; If we want to implement it self-contained, we could use the prime decomposition routine from the Prime_decomposition task. This is reasonably fast and small, though much slower than the modules and certainly could have more optimization. sub factors { my($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.

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;
Output:
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 -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( $n == 1 ) { print "\n"; next N; } print " × "; } } die "Ran out of primes?!"; } ## Perl 6 Works with: rakudo version 2015-10-01 constant @primes = 2, |(3, 5, 7 ... *).grep: *.is-prime; multi factors(1) { 1 } multi factors(Int$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($_).join(" × ") for 1..*; The first twenty numbers: 1: 1 2: 2 3: 3 4: 2 × 2 5: 5 6: 2 × 3 7: 7 8: 2 × 2 × 2 9: 3 × 3 10: 2 × 5 11: 11 12: 2 × 2 × 3 13: 13 14: 2 × 7 15: 3 × 5 16: 2 × 2 × 2 × 2 17: 17 18: 2 × 3 × 3 19: 19 20: 2 × 2 × 5 Here we use a multi declaration with a constant parameter to match the degenerate case. We use copy parameters when we wish to reuse the formal parameter as a mutable variable within the function. (Parameters default to readonly in Perl 6.) Note the use of gather/take as the final statement in the function, which is a common Perl 6 idiom to set up a coroutine within a function to return a lazy list on demand. Note also the '×' above is not ASCII 'x', but U+00D7 MULTIPLICATION SIGN. Perl 6 does Unicode natively. Here is a solution inspired from Almost_prime#C. It doesn't use &is-prime. sub factor($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;

## 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
Output:
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.

(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)) ) )

(for N 20
(prinl N ": " (glue " * " (factor N))) )
Output:
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

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:

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

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:

2 x 2 x 2 x 2 x 2 x 67
2 x 2 x 5 x 5
2 x 2 x 3

## PureBasic

Procedure Factorize(Number, List Factors())
Protected I = 3, Max
ClearList(Factors())
While Number % 2 = 0
Factors() = 2
Number / 2
Wend
Max = Number
While I <= Max And Number > 1
While Number % I = 0
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 Output: 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 functools.lru_cache standard library module to cache intermediate results. 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()) Output: 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 #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) Output: [1] "3 x 3 x 2 x 2 x 2 x 1" ## Racket See also #Scheme. This uses Racket’s math/number-theory package #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 Output: 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 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 low high . /*get optional arguments from the C.L. */ if low=='' then do; low=1; high=40; end /*No LOW & HIGH? Then use the default.*/ if high=='' then high=low; tell= (high>0) /*No HIGH? " " " " */ w=length(high); high=abs(high) /*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=low to high; f=factr(n) /*process a single number or a range.*/ p=words(translate(f,,'x')) - (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 space(f, 0) /*show if prime and 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; parse arg z 1 n,$; if z<2 then return z /*if Z too small, return Z*/
do while z// 2==0; $=$ 'x 2' ; z=z% 2; end /*maybe add factor of 2 */
do while z// 3==0; $=$ 'x 3' ; z=z% 3; end /* " " " " 3 */
do while z// 5==0; $=$ 'x 5' ; z=z% 5; end /* " " " " 5 */
do while z// 7==0; $=$ 'x 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; $=$ 'x' j; z=z%j; end /*maybe reduce Z.*/
if _ ==3 then iterate /*if next number will be ÷ by 5, skip.*/
if j*j>n then leave /*are we higher than the √ N  ? */
y=j+2
do while z//y==0; $=$ 'x' y; z=z%y; end /*maybe reduce Z.*/
end /*j*/

if z==1 then z= /*if residual is unity, then nullify it*/
return strip( strip($'x' z), , "x") /*elide a possible leading (extra) "x".*/ output when using the default inputs: 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. output when the following input was used: 1 -10000 1229 primes found. output when the following input was used: 1 -100000 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 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 low high . /*get optional arguments from the C.L. */ if low=='' then do; low=1; high=40; end /*No LOW & HIGH? Then use the default.*/ if high=='' then high=low; tell= (high>0) /*No HIGH? " " " " */ w=length(high); high=abs(high) /*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=low to high; f=factr(n) /*process a single number or a range.*/ p=words(translate(f,,'x')) - (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 space(f, 0) /*show if prime & the 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; parse arg z 1 n,$; if z<2 then return z /*if Z too small, return Z*/
do while z// 2==0; $=$ 'x 2'  ; z=z% 2; end /*maybe add factor of 2 */
do while z// 3==0; $=$ 'x 3'  ; z=z% 3; end /* " " " " 3 */
do while z// 5==0; $=$ 'x 5'  ; z=z% 5; end /* " " " " 5 */
do while z// 7==0; $=$ 'x 7'  ; z=z% 7; end /* " " " " 7 */
do while z//11==0; $=$ 'x 11' ; z=z%11; end /* " " " " 11 */
do while z//13==0; $=$ 'x 13' ; z=z%13; end /* " " " " 13 */
do while z//17==0; $=$ 'x 17' ; z=z%17; end /* " " " " 17 */
do while z//19==0; $=$ 'x 19' ; z=z%19; end /* " " " " 19 */
do while z//23==0; $=$ 'x 23' ; z=z%23; end /* " " " " 23 */
do while z//29==0; $=$ 'x 29' ; z=z%29; end /* " " " " 29 */
do while z//31==0; $=$ 'x 31' ; z=z%31; end /* " " " " 31 */
do while z//37==0; $=$ 'x 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 /*R: will be integer SQRT of Z.*/

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). */

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; $=$ 'x' j; z=z%j; end /*reduce Z?*/
if _ ==3 then iterate /*Next number ÷ by 5 ? Skip.*/
y=j+2
do while z//y==0; $=$ 'x' y; z=z%y; end /*reduce Z?*/
end /*j*/
end /*if z>40*/

if z==1 then z= /*if residual is unity, then nullify it*/
return strip(strip( $'x' z), , "x") /*elide a possible leading (extra) "x".*/ output is identical to the 1st REXX version. ## 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: 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. 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 Example:$ ruby prime-count.rb -h
Usage: prime-count.rb [-m MAXIMUM]
-m MAXIMUM                       Count up to MAXIMUM [10]
$ruby prime-count.rb -m 10000 | sed -e '11,9990d' 1 is 1 2 is 2 3 is 3 4 is 2 x 2 5 is 5 6 is 2 x 3 7 is 7 8 is 2 x 2 x 2 9 is 3 x 3 10 is 2 x 5 9991 is 97 x 103 9992 is 2 x 2 x 2 x 1249 9993 is 3 x 3331 9994 is 2 x 19 x 263 9995 is 5 x 1999 9996 is 2 x 2 x 3 x 7 x 7 x 17 9997 is 13 x 769 9998 is 2 x 4999 9999 is 3 x 3 x 11 x 101 10000 is 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 ## Run BASIC for i = 1000 to 1016 print i;" = "; factorial$(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
Output:
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

## Scala

def primeFactors( n:Int ) = {

def primeStream(s: Stream[Int]): Stream[Int] = {
}

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(" * ") ) ) )
}

Output:
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

(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))))
Output:
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
...

$include "seed7_05.s7i"; const proc: writePrimeFactors (in var integer: number) is func local var boolean: laterElement is FALSE; var integer: checker is 2; begin while checker * checker <= number do if number rem checker = 0 then if laterElement then write(" * "); end if; laterElement := TRUE; write(checker); number := number div checker; else incr(checker); end if; end while; if number <> 1 then if laterElement then write(" * "); end if; laterElement := TRUE; write(number); end if; end func; const proc: main is func local var integer: number is 0; begin writeln("1: 1"); for number range 2 to 2147483647 do write(number <& ": "); writePrimeFactors(number); writeln; end for; end func; Output: 1: 1 2: 2 3: 3 4: 2 * 2 5: 5 6: 2 * 3 7: 7 8: 2 * 2 * 2 9: 3 * 3 10: 2 * 5 11: 11 12: 2 * 2 * 3 13: 13 14: 2 * 7 15: 3 * 5 . . . ## Sidef class Counter { method factors(n, p=2) { var a = gather { while (n >= p*p) { while (p divides` n) { take(p) n //= p } p = self.next_prime(p) } } (n > 1 || a.is_empty) ? (a << n) : a } method is_prime(n) { self.factors(n).len == 1 } method next_prime(p) { do { p == 2 ? (p = 3) : (p+=2) } while (!self.is_prime(p)) return p } } for i in (1..100) { say "#{i} = #{Counter().factors(i).join(' × ')}" } ## Tcl This factorization code is based on the same engine that is used in the parallel computation task. package require Tcl 8.5 namespace eval prime { variable primes [list 2 3 5 7 11] proc restart {} { variable index -1 variable primes variable current [lindex$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:

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. 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 Output: 2 = 2 2144 = 2 * 2 * 2 * 2 * 2 * 67 ## Visual Basic .NET 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 Output: 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 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: 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 foreach n in ([1..*]){ println(n,": ",primeFactors(n).concat("\U2715;")) } Using the fixed size integer (64 bit) solution from Prime decomposition#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; } Output: 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 Translation of: BBC_BASIC 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