Factors of an integer

From Rosetta Code
Task
Factors of an integer
You are encouraged to solve this task according to the task description, using any language you may know.

Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.

You may see other such operations in the Basic Data Operations category, or:

Integer Operations
Arithmetic | Comparison

Boolean Operations
Bitwise | Logical

String Operations
Concatenation | Interpolation | Comparison | Matching

Memory Operations
Pointers & references | Addresses

Compute the factors of a positive integer. These factors are the positive integers by which the number being factored can be divided to yield a positive integer result. (Though the concepts function correctly for zero and negative integers, the set of factors of zero has countably infinite members, and the factors of negative integers can be obtained from the factors of related positive numbers without difficulty; this task does not require handling of either of these cases). Note that every prime number has two factors; ‘1’ and itself.

See also:

Contents

0815[edit]

 
<:1:~>|~#:end:>~x}:str:/={^:wei:~%x<:a:x=$~
=}:wei:x<:1:+{>~>x=-#:fin:^:str:}:fin:{{~%
 

360 Assembly[edit]

Very compact version.

*        Factors of an integer -   07/10/2015
FACTOR CSECT
USING FACTOR,R15 set base register
LA R7,PG pgi=@pg
LA R6,1 i
L R3,N loop count
LOOP L R5,N n
LA R4,0
DR R4,R6 n/i
LTR R4,R4 if mod(n,i)=0
BNZ NEXT
XDECO R6,PG+120 edit i
MVC 0(6,R7),PG+126 output i
LA R7,6(R7) pgi=pgi+6
NEXT LA R6,1(R6) i=i+1
BCT R3,LOOP loop
XPRNT PG,120 print buffer
XR R15,R15 set return code
BR R14 return to caller
N DC F'12345' <== input value
PG DC CL132' ' buffer
YREGS
END FACTOR
Output:
     1     3     5    15   823  2469  4115 12345

ACL2[edit]

(defun factors-r (n i)
(declare (xargs :measure (nfix (- n i))))
(cond ((zp (- n i))
(list n))
((= (mod n i) 0)
(cons i (factors-r n (1+ i))))
(t (factors-r n (1+ i)))))
 
(defun factors (n)
(factors-r n 1))

ActionScript[edit]

function factor(n:uint):Vector.<uint>
{
var factors:Vector.<uint> = new Vector.<uint>();
for(var i:uint = 1; i <= n; i++)
if(n % i == 0)factors.push(i);
return factors;
}

Ada[edit]

with Ada.Text_IO;
with Ada.Command_Line;
procedure Factors is
Number  : Positive;
Test_Nr : Positive := 1;
begin
if Ada.Command_Line.Argument_Count /= 1 then
Ada.Text_IO.Put (Ada.Text_IO.Standard_Error, "Missing argument!");
Ada.Command_Line.Set_Exit_Status (Ada.Command_Line.Failure);
return;
end if;
Number := Positive'Value (Ada.Command_Line.Argument (1));
Ada.Text_IO.Put ("Factors of" & Positive'Image (Number) & ": ");
loop
if Number mod Test_Nr = 0 then
Ada.Text_IO.Put (Positive'Image (Test_Nr) & ",");
end if;
exit when Test_Nr ** 2 >= Number;
Test_Nr := Test_Nr + 1;
end loop;
Ada.Text_IO.Put_Line (Positive'Image (Number) & ".");
end Factors;

Aikido[edit]

import math
 
function factor (n:int) {
var result = []
function append (v) {
if (!(v in result)) {
result.append (v)
}
}
var sqrt = cast<int>(Math.sqrt (n))
append (1)
for (var i = n-1 ; i >= sqrt ; i--) {
if ((n % i) == 0) {
append (i)
append (n/i)
}
}
append (n)
return result.sort()
}
 
function printvec (vec) {
var comma = ""
print ("[")
foreach v vec {
print (comma + v)
comma = ", "
}
println ("]")
}
 
printvec (factor (45))
printvec (factor (25))
printvec (factor (100))

ALGOL 68[edit]

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d

Note: The following implements generators, eliminating the need of declaring arbitrarily long int arrays for caching.

MODE YIELDINT = PROC(INT)VOID;
 
PROC gen factors = (INT n, YIELDINT yield)VOID: (
FOR i FROM 1 TO ENTIER sqrt(n) DO
IF n MOD i = 0 THEN
yield(i);
INT other = n OVER i;
IF i NE other THEN yield(n OVER i) FI
FI
OD
);
 
[]INT nums2factor = (45, 53, 64);
 
FOR i TO UPB nums2factor DO
INT num = nums2factor[i];
STRING sep := ": ";
print(num);
# FOR INT j IN # gen factors(num, # ) DO ( #
## (INT j)VOID:(
print((sep,whole(j,0)));
sep:=", "
# OD # ));
print(new line)
OD
Output:
        +45: 1, 45, 3, 15, 5, 9
        +53: 1, 53
        +64: 1, 64, 2, 32, 4, 16, 8

ALGOL W[edit]

begin
 % return the factors of n ( n should be >= 1 ) in the array factor  %
 % the bounds of factor should be 0 :: len (len must be at least 1)  %
 % the number of factors will be returned in factor( 0 )  %
procedure getFactorsOf ( integer value n
 ; integer array factor( * )
 ; integer value len
) ;
begin
for i := 0 until len do factor( i ) := 0;
if n >= 1 and len >= 1 then begin
integer pos, lastFactor;
factor( 0 ) := factor( 1 ) := pos := 1;
 % find the factors up to sqrt( n )  %
for f := 2 until truncate( sqrt( n ) ) + 1 do begin
if ( n rem f ) = 0 and pos <= len then begin
 % found another factor and there's room to store it  %
pos  := pos + 1;
factor( 0 ) := pos;
factor( pos ) := f
end if_found_factor
end for_f;
 % find the factors above sqrt( n )  %
lastFactor := factor( factor( 0 ) );
for f := factor( 0 ) step -1 until 1 do begin
integer newFactor;
newFactor := n div factor( f );
if newFactor > lastFactor and pos <= len then begin
 % found another factor and there's room to store it  %
pos  := pos + 1;
factor( 0 ) := pos;
factor( pos ) := newFactor
end if_found_factor
end for_f;
end if_params_ok
end getFactorsOf ;
 
 
 % prpocedure to test getFactorsOf  %
procedure testFactorsOf( integer value n ) ;
begin
integer array factor( 0 :: 100 );
getFactorsOf( n, factor, 100 );
i_w := 1; s_w := 0; % set output format  %
write( n, " has ", factor( 0 ), " factors:" );
for f := 1 until factor( 0 ) do writeon( " ", factor( f ) )
end testFactorsOf ;
 
 % test the factorising  %
for i := 1 until 100 do testFactorsOf( i )
 
end.
Output:
1 has 1 factors: 1
2 has 2 factors: 1 2
3 has 2 factors: 1 3
4 has 3 factors: 1 2 4
...
96 has 12 factors: 1 2 3 4 6 8 12 16 24 32 48 96
97 has 2 factors: 1 97
98 has 6 factors: 1 2 7 14 49 98
99 has 6 factors: 1 3 9 11 33 99
100 has 9 factors: 1 2 4 5 10 20 25 50 100

APL[edit]

      factors←{(0=(⍳⍵)|⍵)/⍳⍵}
factors 12345
1 3 5 15 823 2469 4115 12345
factors 720
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720

AutoHotkey[edit]

msgbox, % factors(45) "`n" factors(53) "`n" factors(64)
 
Factors(n)
{ Loop, % floor(sqrt(n))
{ v := A_Index = 1 ? 1 "," n : mod(n,A_Index) ? v : v "," A_Index "," n//A_Index
}
Sort, v, N U D,
Return, v
}
Output:
1,3,5,9,15,45
1,53
1,2,4,8,16,32,64

AutoIt[edit]

;AutoIt Version: 3.2.10.0
$num = 45
MsgBox (0,"Factors", "Factors of " & $num & " are: " & factors($num))
consolewrite ("Factors of " & $num & " are: " & factors($num))
Func factors($intg)
$ls_factors=""
For $i = 1 to $intg/2
if ($intg/$i - int($intg/$i))=0 Then
$ls_factors=$ls_factors&$i &", "
EndIf
Next
Return $ls_factors&$intg
EndFunc
Output:
Factors of 45 are: 1, 3, 5, 9, 15, 45

AWK[edit]

 
# syntax: GAWK -f FACTORS_OF_AN_INTEGER.AWK
BEGIN {
print("enter a number or C/R to exit")
}
{ if ($0 == "") { exit(0) }
if ($0 !~ /^[0-9]+$/) {
printf("invalid: %s\n",$0)
next
}
n = $0
printf("factors of %s:",n)
for (i=1; i<=n; i++) {
if (n % i == 0) {
printf(" %d",i)
}
}
printf("\n")
}
 
Output:
enter a number or C/R to exit
invalid: -1
factors of 0:
factors of 1: 1
factors of 2: 1 2
factors of 11: 1 11
factors of 64: 1 2 4 8 16 32 64
factors of 100: 1 2 4 5 10 20 25 50 100
factors of 32766: 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766
factors of 32767: 1 7 31 151 217 1057 4681 32767

BASIC[edit]

Works with: QBasic

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

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

DECLARE SUB factor (what AS INTEGER)
 
REDIM SHARED factors(0) AS INTEGER
 
DIM i AS INTEGER, L AS INTEGER
 
INPUT "Gimme a number"; i
 
factor i
 
PRINT factors(0);
FOR L = 1 TO UBOUND(factors)
PRINT ","; factors(L);
NEXT
PRINT
 
SUB factor (what AS INTEGER)
DIM tmpint1 AS INTEGER
DIM L0 AS INTEGER, L1 AS INTEGER
 
REDIM tmp(0) AS INTEGER
REDIM factors(0) AS INTEGER
factors(0) = 1
 
FOR L0 = 2 TO what
IF (0 = (what MOD L0)) THEN
'all this REDIMing and copying can be replaced with:
'REDIM PRESERVE factors(UBOUND(factors)+1)
'in languages that support the PRESERVE keyword
REDIM tmp(UBOUND(factors)) AS INTEGER
FOR L1 = 0 TO UBOUND(factors)
tmp(L1) = factors(L1)
NEXT
REDIM factors(UBOUND(factors) + 1)
FOR L1 = 0 TO UBOUND(factors) - 1
factors(L1) = tmp(L1)
NEXT
factors(UBOUND(factors)) = L0
END IF
NEXT
END SUB
Output:
 Gimme a number? 17
  1 , 17
 Gimme a number? 12345
  1 , 3 , 5 , 15 , 823 , 2469 , 4115 , 12345
 Gimme a number? 32765
  1 , 5 , 6553 , 32765
 Gimme a number? 32766
  1 , 2 , 3 , 6 , 43 , 86 , 127 , 129 , 254 , 258 , 381 , 762 , 5461 , 10922 ,
  16383 , 32766

Batch File[edit]

Command line version:

@echo off
set res=Factors of %1:
for /L %%i in (1,1,%1) do call :fac %1 %%i
echo %res%
goto :eof
 
:fac
set /a test = %1 %% %2
if %test% equ 0 set res=%res% %2
Output:
>factors 32767
Factors of 32767: 1 7 31 151 217 1057 4681 32767

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

>factors 53
Factors of 53: 1 53

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

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

Interactive version:

@echo off
set /p limit=Gimme a number:
set res=Factors of %limit%:
for /L %%i in (1,1,%limit%) do call :fac %limit% %%i
echo %res%
goto :eof
 
:fac
set /a test = %1 %% %2
if %test% equ 0 set res=%res% %2
Output:
>factors
Gimme a number:27
Factors of 27: 1 3 9 27

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

BBC BASIC[edit]

      INSTALL @lib$+"SORTLIB"
sort% = FN_sortinit(0, 0)
 
PRINT "The factors of 45 are " FNfactorlist(45)
PRINT "The factors of 12345 are " FNfactorlist(12345)
END
 
DEF FNfactorlist(N%)
LOCAL C%, I%, L%(), L$
DIM L%(32)
FOR I% = 1 TO SQR(N%)
IF (N% MOD I% = 0) THEN
L%(C%) = I%
C% += 1
IF (N% <> I%^2) THEN
L%(C%) = (N% DIV I%)
C% += 1
ENDIF
ENDIF
NEXT I%
CALL sort%, L%(0)
FOR I% = 0 TO C%-1
L$ += STR$(L%(I%)) + ", "
NEXT
= LEFT$(LEFT$(L$))
Output:
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345

bc[edit]

/* Calculate the factors of n and return their count.
* This function mutates the global array f[] which will
* contain all factors of n in ascending order after the call!
*/
define f(n) {
auto i, d, h, h[], l, o
/* Local variables:
* i: Loop variable.
* d: Complementary (higher) factor to i.
* h: Will always point to the last element of h[].
* h[]: Array to hold the greater factor of the pair (x, y), where
* x * y == n. The factors are stored in descending order.
* l: Will always point to the next free spot in f[].
* o: For saving the value of scale.
*/
 
/* Use integer arithmetic */
o = scale
scale = 0
 
/* Two factors are 1 and n (if n != 1) */
f[l++] = 1
if (n == 1) return(1)
h[0] = n
 
/* Main loop */
for (i = 2; i < h[h]; i++) {
if (n % i == 0) {
d = n / i
if (d != i) {
h[++h] = d
}
f[l++] = i
}
}
 
/* Append the values in h[] to f[] */
while (h >= 0) {
f[l++] = h[h--]
}
 
scale = o
return(l)
}

Befunge[edit]

10:p&v:      >:0:g%#v_0:g\:0:g/\v
>:0:g:*`| > >0:g1+0:p
>:0:g:*-#v_0:g\>$>:!#@_.v
> ^ ^ ," "<

C[edit]

#include <stdio.h>
#include <stdlib.h>
 
typedef struct {
int *list;
short count;
} Factors;
 
void xferFactors( Factors *fctrs, int *flist, int flix )
{
int ix, ij;
int newSize = fctrs->count + flix;
if (newSize > flix) {
fctrs->list = realloc( fctrs->list, newSize * sizeof(int));
}
else {
fctrs->list = malloc( newSize * sizeof(int));
}
for (ij=0,ix=fctrs->count; ix<newSize; ij++,ix++) {
fctrs->list[ix] = flist[ij];
}
fctrs->count = newSize;
}
 
Factors *factor( int num, Factors *fctrs)
{
int flist[301], flix;
int dvsr;
flix = 0;
fctrs->count = 0;
free(fctrs->list);
fctrs->list = NULL;
for (dvsr=1; dvsr*dvsr < num; dvsr++) {
if (num % dvsr != 0) continue;
if ( flix == 300) {
xferFactors( fctrs, flist, flix );
flix = 0;
}
flist[flix++] = dvsr;
flist[flix++] = num/dvsr;
}
if (dvsr*dvsr == num)
flist[flix++] = dvsr;
if (flix > 0)
xferFactors( fctrs, flist, flix );
 
return fctrs;
}
 
int main(int argc, char*argv[])
{
int nums2factor[] = { 2059, 223092870, 3135, 45 };
Factors ftors = { NULL, 0};
char sep;
int i,j;
 
for (i=0; i<4; i++) {
factor( nums2factor[i], &ftors );
printf("\nfactors of %d are:\n ", nums2factor[i]);
sep = ' ';
for (j=0; j<ftors.count; j++) {
printf("%c %d", sep, ftors.list[j]);
sep = ',';
}
printf("\n");
}
return 0;
}

Prime factoring[edit]

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
 
/* 65536 = 2^16, so we can factor all 32 bit ints */
char bits[65536];
 
typedef unsigned long ulong;
ulong primes[7000], n_primes;
 
typedef struct { ulong p, e; } prime_factor; /* prime, exponent */
 
void sieve()
{
int i, j;
memset(bits, 1, 65536);
bits[0] = bits[1] = 0;
for (i = 0; i < 256; i++)
if (bits[i])
for (j = i * i; j < 65536; j += i)
bits[j] = 0;
 
/* collect primes into a list. slightly faster this way if dealing with large numbers */
for (i = j = 0; i < 65536; i++)
if (bits[i]) primes[j++] = i;
 
n_primes = j;
}
 
int get_prime_factors(ulong n, prime_factor *lst)
{
ulong i, e, p;
int len = 0;
 
for (i = 0; i < n_primes; i++) {
p = primes[i];
if (p * p > n) break;
for (e = 0; !(n % p); n /= p, e++);
if (e) {
lst[len].p = p;
lst[len++].e = e;
}
}
 
return n == 1 ? len : (lst[len].p = n, lst[len].e = 1, ++len);
}
 
int ulong_cmp(const void *a, const void *b)
{
return *(const ulong*)a < *(const ulong*)b ? -1 : *(const ulong*)a > *(const ulong*)b;
}
 
int get_factors(ulong n, ulong *lst)
{
int n_f, len, len2, i, j, k, p;
prime_factor f[100];
 
n_f = get_prime_factors(n, f);
 
len2 = len = lst[0] = 1;
/* L = (1); L = (L, L * p**(1 .. e)) forall((p, e)) */
for (i = 0; i < n_f; i++, len2 = len)
for (j = 0, p = f[i].p; j < f[i].e; j++, p *= f[i].p)
for (k = 0; k < len2; k++)
lst[len++] = lst[k] * p;
 
qsort(lst, len, sizeof(ulong), ulong_cmp);
return len;
}
 
int main()
{
ulong fac[10000];
int len, i, j;
ulong nums[] = {3, 120, 1024, 2UL*2*2*2*3*3*3*5*5*7*11*13*17*19 };
 
sieve();
 
for (i = 0; i < 4; i++) {
len = get_factors(nums[i], fac);
printf("%lu:", nums[i]);
for (j = 0; j < len; j++)
printf(" %lu", fac[j]);
printf("\n");
}
 
return 0;
}
Output:
3: 1 3
120: 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
1024: 1 2 4 8 16 32 64 128 256 512 1024
3491888400: 1 2 3 4 5 6 7 8 9 10 11 ...(>1900 numbers)... 1163962800 1745944200 3491888400

C++[edit]

#include <iostream>
#include <vector>
#include <algorithm>
#include <iterator>
 
std::vector<int> GenerateFactors(int n)
{
std::vector<int> factors;
factors.push_back(1);
factors.push_back(n);
for(int i = 2; i * i <= n; ++i)
{
if(n % i == 0)
{
factors.push_back(i);
if(i * i != n)
factors.push_back(n / i);
}
}
 
std::sort(factors.begin(), factors.end());
return factors;
}
 
int main()
{
const int SampleNumbers[] = {3135, 45, 60, 81};
 
for(size_t i = 0; i < sizeof(SampleNumbers) / sizeof(int); ++i)
{
std::vector<int> factors = GenerateFactors(SampleNumbers[i]);
std::cout << "Factors of " << SampleNumbers[i] << " are:\n";
std::copy(factors.begin(), factors.end(), std::ostream_iterator<int>(std::cout, "\n"));
std::cout << std::endl;
}
}

C#[edit]

C# 3.0

using System;
using System.Linq;
using System.Collections.Generic;
 
public static class Extension
{
public static List<int> Factors(this int me)
{
return Enumerable.Range(1, me).Where(x => me % x == 0).ToList();
}
}
 
class Program
{
static void Main(string[] args)
{
Console.WriteLine(String.Join(", ", 45.Factors()));
}
}

C# 1.0

static void Main(string[] args)
{
do
{
Console.WriteLine("Number:");
Int64 p = 0;
do
{
try
{
p = Convert.ToInt64(Console.ReadLine());
break;
}
catch (Exception)
{ }
 
} while (true);
 
Console.WriteLine("For 1 through " + ((int)Math.Sqrt(p)).ToString() + "");
for (int x = 1; x <= (int)Math.Sqrt(p); x++)
{
if (p % x == 0)
Console.WriteLine("Found: " + x.ToString() + ". " + p.ToString() + " / " + x.ToString() + " = " + (p / x).ToString());
}
 
Console.WriteLine("Done.");
} while (true);
}
Output:
Number:
32434243
For 1 through 5695
Found: 1. 32434243 / 1 = 32434243
Found: 307. 32434243 / 307 = 105649
Done.

Ceylon[edit]

shared void run() {
{Integer*} getFactors(Integer n) =>
(1..n).filter((Integer element) => element.divides(n));
 
for(Integer i in 1..100) {
print("the factors of ``i`` are ``getFactors(i)``");
}
}

Chapel[edit]

Inspired by the Clojure solution:

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

Clojure[edit]

(defn factors [n] 
(filter #(zero? (rem n %)) (range 1 (inc n))))
 
(print (factors 45))
(1 3 5 9 15 45)

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

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

Same idea, using for comprehensions.

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

CoffeeScript[edit]

# Reference implementation for finding factors is slow, but hopefully
# robust--we'll use it to verify the more complicated (but hopefully faster)
# algorithm.
slow_factors = (n) ->
(i for i in [1..n] when n % i == 0)
 
# The rest of this code does two optimizations:
# 1) When you find a prime factor, divide it out of n (smallest_prime_factor).
# 2) Find the prime factorization first, then compute composite factors from those.
 
smallest_prime_factor = (n) ->
for i in [2..n]
return n if i*i > n
return i if n % i == 0
 
prime_factors = (n) ->
return {} if n == 1
spf = smallest_prime_factor n
result = prime_factors(n / spf)
result[spf] or= 0
result[spf] += 1
result
 
fast_factors = (n) ->
prime_hash = prime_factors n
exponents = []
for p of prime_hash
exponents.push
p: p
exp: 0
result = []
while true
factor = 1
for obj in exponents
factor *= Math.pow obj.p, obj.exp
result.push factor
break if factor == n
# roll the odometer
for obj, i in exponents
if obj.exp < prime_hash[obj.p]
obj.exp += 1
break
else
obj.exp = 0
 
return result.sort (a, b) -> a - b
 
verify_factors = (factors, n) ->
expected_result = slow_factors n
throw Error("wrong length") if factors.length != expected_result.length
for factor, i in expected_result
console.log Error("wrong value") if factors[i] != factor
 
 
for n in [1, 3, 4, 8, 24, 37, 1001, 11111111111, 99999999999]
factors = fast_factors n
console.log n, factors
if n < 1000000
verify_factors factors, n
Output:
> coffee factors.coffee 
1 [ 1 ]
3 [ 1, 3 ]
4 [ 1, 2, 4 ]
8 [ 1, 2, 4, 8 ]
24 [ 1, 2, 3, 4, 6, 8, 12, 24 ]
37 [ 1, 37 ]
1001 [ 1, 7, 11, 13, 77, 91, 143, 1001 ]
11111111111 [ 1, 21649, 513239, 11111111111 ]
99999999999 [ 1,
  3,
  9,
  21649,
  64947,
  194841,
  513239,
  1539717,
  4619151,
  11111111111,
  33333333333,
  99999999999 ]

Common Lisp[edit]

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

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

D[edit]

Procedural Style[edit]

import std.stdio, std.math, std.algorithm;
 
T[] factors(T)(in T n) pure nothrow {
if (n == 1)
return [n];
 
T[] res = [1, n];
T limit = cast(T)real(n).sqrt + 1;
for (T i = 2; i < limit; i++) {
if (n % i == 0) {
res ~= i;
immutable q = n / i;
if (q > i)
res ~= q;
}
}
 
return res.sort().release;
}
 
void main() {
writefln("%(%s\n%)", [45, 53, 64, 1111111].map!factors);
}
Output:
[1, 3, 5, 9, 15, 45]
[1, 53]
[1, 2, 4, 8, 16, 32, 64]
[1, 239, 4649, 1111111]

Functional Style[edit]

import std.stdio, std.algorithm, std.range;
 
auto factors(I)(I n) {
return iota(1, n + 1).filter!(i => n % i == 0);
}
 
void main() {
36.factors.writeln;
}
Output:
[1, 2, 3, 4, 6, 9, 12, 18, 36]

E[edit]

This example is in need of improvement:
Use a cleverer algorithm such as in the Common Lisp example.
def factors(x :(int > 0)) {
var xfactors := []
for f ? (x % f <=> 0) in 1..x {
xfactors with= f
}
return xfactors
}

EchoLisp[edit]

prime-factors gives the list of n's prime-factors. We mix them to get all the factors.

 
;; ppows
;; input : a list g of grouped prime factors ( 3 3 3 ..)
;; returns (1 3 9 27 ...)
 
(define (ppows g (mult 1))
(for/fold (ppows '(1)) ((a g))
(set! mult (* mult a))
(cons mult ppows)))
 
;; factors
;; decomp n into ((2 2 ..) ( 3 3 ..) ) prime factors groups
;; combines (1 2 4 8 ..) (1 3 9 ..) lists
 
(define (factors n)
(list-sort <
(if (<= n 1) '(1)
(for/fold (divs'(1)) ((g (map ppows (group (prime-factors n)))))
(for*/list ((a divs) (b g)) (* a b))))))
 
Output:
 
(lib 'bigint)
(factors 666)
(1 2 3 6 9 18 37 74 111 222 333 666)
 
(length (factors 108233175859200))
666 ;; 💀
 
(define huge 1200034005600070000008900000000000000000)
(time ( length (factors huge)))
(394ms 7776)
 

Ela[edit]

Using higher-order function[edit]

open list
 
factors m = filter (\x -> m % x == 0) [1..m]

Using comprehension[edit]

factors m = [x \\ x <- [1..m] | m % x == 0]

Elixir[edit]

defmodule RC do
def factor(1), do: [1]
def factor(n) do
(for i <- 1..div(n,2), rem(n,i)==0, do: i) ++ [n]
end
end
 
Enum.each([45, 53, 64], fn n ->
IO.puts "#{n}: #{inspect RC.factor(n)}"
end)
Output:
45: [1, 3, 5, 9, 15, 45]
53: [1, 53]
64: [1, 2, 4, 8, 16, 32, 64]

Erlang[edit]

with Built in fuctions[edit]

factors(N) ->
[I || I <- lists:seq(1,trunc(N/2)), N rem I == 0]++[N].

Recursive[edit]

Another, less concise, but faster version

 
 
-module(divs).
-export([divs/1]).
 
divs(0) -> [];
divs(1) -> [];
divs(N) -> lists:sort(divisors(1,N))++[N].
 
divisors(1,N) ->
[1] ++ divisors(2,N,math:sqrt(N)).
 
divisors(K,_N,Q) when K > Q -> [];
divisors(K,N,_Q) when N rem K =/= 0 ->
[] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) when K * K == N ->
[K] ++ divisors(K+1,N,math:sqrt(N));
divisors(K,N,_Q) ->
[K, N div K] ++ divisors(K+1,N,math:sqrt(N)).
 
Output:
58> timer:tc(divs, factors, [20000]).
{2237,
 [1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,
  500,625,800,1000,1250,2000,2500,4000|...]}
59> timer:tc(divs, divs, [20000]).   
{106,
 [1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,
  500,625,800,1000,1250,2000,2500,4000|...]}

The first number is milliseconds. I'v ommitted repeating the first fuction.

ERRE[edit]

 
PROGRAM FACTORS
 
!$DOUBLE
 
PROCEDURE FACTORLIST(N->L$)
 
LOCAL C%,I,FLIPS%,I%
LOCAL DIM L[32]
FOR I=1 TO SQR(N) DO
IF N=I*INT(N/I) THEN
L[C%]=I
C%=C%+1
IF N<>I*I THEN
L[C%]=INT(N/I)
C%=C%+1
END IF
END IF
END FOR
 
 ! BUBBLE SORT ARRAY L[]
FLIPS%=1
WHILE FLIPS%>0 DO
FLIPS%=0
FOR I%=0 TO C%-2 DO
IF L[I%]>L[I%+1] THEN SWAP(L[I%],L[I%+1]) FLIPS%=1
END FOR
END WHILE
 
L$=""
FOR I%=0 TO C%-1 DO
L$=L$+STR$(L[I%])+","
END FOR
L$=LEFT$(L$,LEN(L$)-1)
 
END PROCEDURE
 
BEGIN
PRINT(CHR$(12);) ! CLS
FACTORLIST(45->L$)
PRINT("The factors of 45 are ";L$)
FACTORLIST(12345->L$)
PRINT("The factors of 12345 are ";L$)
END PROGRAM
 
Output:
The factors of 45 are  1, 3, 5, 9, 15, 45
The factors of 12345 are  1, 3, 5, 15, 823, 2469, 4115, 12345

F#[edit]

If number % divisor = 0 then both divisor AND number / divisor are factors.

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

Also, this is lazily evaluated.

let factors number = seq {
for divisor in 1 .. (float >> sqrt >> int) number do
if number % divisor = 0 then
yield divisor
yield number / divisor
}

Factor[edit]

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

FALSE[edit]

[1[\$@$@-][\$@$@$@$@\/*=[$." "]?1+]#.%]f:
45f;! 53f;! 64f;!

Forth[edit]

This is a slightly optimized algorithm, since it realizes there are no factors between n/2 and n. The values are saved on the stack and - in true Forth fashion - printed in descending order.

: factors dup 2/ 1+ 1 do dup i mod 0= if i swap then loop ;
: .factors factors begin dup dup . 1 <> while drop repeat drop cr ;
 
45 .factors
53 .factors
64 .factors
100 .factors

Fortran[edit]

Works with: Fortran version 90 and later
program Factors
implicit none
integer :: i, number
 
write(*,*) "Enter a number between 1 and 2147483647"
read*, number
 
do i = 1, int(sqrt(real(number))) - 1
if (mod(number, i) == 0) write (*,*) i, number/i
end do
 
! Check to see if number is a square
i = int(sqrt(real(number)))
if (i*i == number) then
write (*,*) i
else if (mod(number, i) == 0) then
write (*,*) i, number/i
end if
 
end program

Frink[edit]

Frink has built-in factoring functions which use wheel factoring, trial division, Pollard p-1 factoring, and Pollard rho factoring. It also recognizes some special forms (e.g. Mersenne numbers) and handles them efficiently. Integers can either be decomposed into prime factors or all factors.

The factors[n] function will return the prime decomposition of n.

The allFactors[n, include1=true, includeN=true, sort=true, onlyToSqrt=false] function will return all factors of n. The optional arguments include1 and includeN indicate if the numbers 1 and n are to be included in the results. If the optional argument sort is true, the results will be sorted. If the optional argument onlyToSqrt=true, then only the factors less than or equal to the square root of the number will be produced.

The following produces all factors of n, including 1 and n:

allFactors[n]

FunL[edit]

Function to compute set of factors:

def factors( n ) = {d | d <- 1..n if d|n}

Test:

for x <- [103, 316, 519, 639, 760]
println( 'The set of factors of ' + x + ' is ' + factors(x) )
Output:
The set of factors of 103 is {1, 103}
The set of factors of 316 is {158, 4, 79, 1, 2, 316}
The set of factors of 519 is {1, 3, 173, 519}
The set of factors of 639 is {9, 639, 71, 213, 1, 3}
The set of factors of 760 is {8, 19, 4, 40, 152, 5, 10, 76, 1, 95, 190, 760, 20, 2, 38, 380}

GAP[edit]

# Built-in function
DivisorsInt(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]
 
# A possible implementation, not suitable to large n
div := n -> Filtered([1 .. n], k -> n mod k = 0);
 
div(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]
 
# Another implementation, usable for large n (if n can be factored quickly)
div2 := function(n)
local f, p;
f := Collected(FactorsInt(n));
p := List(f, v -> List([0 .. v[2]], k -> v[1]^k));
return SortedList(List(Cartesian(p), Product));
end;
 
div2(Factorial(5));
# [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 ]

Go[edit]

Trial division, no prime number generator, but with some optimizations. It's good enough to factor any 64 bit integer, with large primes taking several seconds.

package main
 
import "fmt"
 
func main() {
printFactors(-1)
printFactors(0)
printFactors(1)
printFactors(2)
printFactors(3)
printFactors(53)
printFactors(45)
printFactors(64)
printFactors(600851475143)
printFactors(999999999999999989)
}
 
func printFactors(nr int64) {
if nr < 1 {
fmt.Println("\nFactors of", nr, "not computed")
return
}
fmt.Printf("\nFactors of %d: ", nr)
fs := make([]int64, 1)
fs[0] = 1
apf := func(p int64, e int) {
n := len(fs)
for i, pp := 0, p; i < e; i, pp = i+1, pp*p {
for j := 0; j < n; j++ {
fs = append(fs, fs[j]*pp)
}
}
}
e := 0
for ; nr & 1 == 0; e++ {
nr >>= 1
}
apf(2, e)
for d := int64(3); nr > 1; d += 2 {
if d*d > nr {
d = nr
}
for e = 0; nr%d == 0; e++ {
nr /= d
}
if e > 0 {
apf(d, e)
}
}
fmt.Println(fs)
fmt.Println("Number of factors =", len(fs))
}
Output:
Factors of -1 not computed

Factors of 0 not computed

Factors of 1: [1]
Number of factors = 1

Factors of 2: [1 2]
Number of factors = 2

Factors of 3: [1 3]
Number of factors = 2

Factors of 53: [1 53]
Number of factors = 2

Factors of 45: [1 3 9 5 15 45]
Number of factors = 6

Factors of 64: [1 2 4 8 16 32 64]
Number of factors = 7

Factors of 600851475143: [1 71 839 59569 1471 104441 1234169 87625999 6857 486847 5753023 408464633 10086647 716151937 8462696833 600851475143]
Number of factors = 16

Factors of 999999999999999989: [1 999999999999999989]
Number of factors = 2

Groovy[edit]

A straight brute force approach up to the square root of N:

def factorize = { long target -> 
 
if (target == 1) return [1L]
 
if (target < 4) return [1L, target]
 
def targetSqrt = Math.sqrt(target)
def lowfactors = (2L..targetSqrt).grep { (target % it) == 0 }
if (lowfactors == []) return [1L, target]
def nhalf = lowfactors.size() - ((lowfactors[-1] == targetSqrt) ? 1 : 0)
 
[1] + lowfactors + (0..<nhalf).collect { target.intdiv(lowfactors[it]) }.reverse() + [target]
}

Test:

((1..30) + [333333]).each { println ([number:it, factors:factorize(it)]) }
Output:
[number:1, factors:[1]]
[number:2, factors:[1, 2]]
[number:3, factors:[1, 3]]
[number:4, factors:[1, 2, 4]]
[number:5, factors:[1, 5]]
[number:6, factors:[1, 2, 3, 6]]
[number:7, factors:[1, 7]]
[number:8, factors:[1, 2, 4, 8]]
[number:9, factors:[1, 3, 9]]
[number:10, factors:[1, 2, 5, 10]]
[number:11, factors:[1, 11]]
[number:12, factors:[1, 2, 3, 4, 6, 12]]
[number:13, factors:[1, 13]]
[number:14, factors:[1, 2, 7, 14]]
[number:15, factors:[1, 3, 5, 15]]
[number:16, factors:[1, 2, 4, 8, 16]]
[number:17, factors:[1, 17]]
[number:18, factors:[1, 2, 3, 6, 9, 18]]
[number:19, factors:[1, 19]]
[number:20, factors:[1, 2, 4, 5, 10, 20]]
[number:21, factors:[1, 3, 7, 21]]
[number:22, factors:[1, 2, 11, 22]]
[number:23, factors:[1, 23]]
[number:24, factors:[1, 2, 3, 4, 6, 8, 12, 24]]
[number:25, factors:[1, 5, 25]]
[number:26, factors:[1, 2, 13, 26]]
[number:27, factors:[1, 3, 9, 27]]
[number:28, factors:[1, 2, 4, 7, 14, 28]]
[number:29, factors:[1, 29]]
[number:30, factors:[1, 2, 3, 5, 6, 10, 15, 30]]
[number:333333, factors:[1, 3, 7, 9, 11, 13, 21, 33, 37, 39, 63, 77, 91, 99, 111, 117, 143, 231, 259, 273, 333, 407, 429, 481, 693, 777, 819, 1001, 1221, 1287, 1443, 2331, 2849, 3003, 3367, 3663, 4329, 5291, 8547, 9009, 10101, 15873, 25641, 30303, 37037, 47619, 111111, 333333]]

Haskell[edit]

Using D. Amos module Primes [1] for finding prime factors

import HFM.Primes(primePowerFactors)
import Data.List
 
factors = map product.
mapM (uncurry((. enumFromTo 0) . map .(^) )) . primePowerFactors

List comprehension[edit]

Naive, functional, no import

factors_naive n = [i | i <-[1..n], (mod n i) == 0]
factors_naive 6
[1,2,3,6]
 

Factor, cofactor. Rearrange a list of tuples to a sorted list

import Data.List
tuple_to_list lt = (fst lt) ++ (snd lt)
factors_co n = sort (tuple_to_list(unzip
[ (j, (div n j)) | j <-
[i | i <-
[1..truncate (sqrt (fromIntegral n))]
, (mod n i) == 0]] ))
 
factors_co 6
[1,2,3,6]
 

A cleaner, simplified version of the code above, without the sorting nor the tuples, increasing speed and making it possible to see results in real time (if using GHCi)

import Data.List
factors n = lows ++ (reverse $ map (div n) lows)
where lows = filter ((== 0) . mod n) [1..truncate . sqrt $ fromIntegral n]
 
*Main> :set +s
*Main> factors 120
[1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120]
(0.01 secs, 7578656 bytes)

HicEst[edit]

 DLG(NameEdit=N, TItle='Enter an integer')
 
DO i = 1, N^0.5
IF( MOD(N,i) == 0) WRITE() i, N/i
ENDDO
 
END

Icon and Unicon[edit]

procedure main(arglist)
numbers := arglist ||| [ 32767, 45, 53, 64, 100] # combine command line provided and default set of values
every writes(lf,"factors of ",i := !numbers,"=") & writes(divisors(i)," ") do lf := "\n"
end
 
link factors
Output:
factors of 32767=1 7 31 151 217 1057 4681 32767
factors of 45=1 3 5 9 15 45
factors of 53=1 53
factors of 64=1 2 4 8 16 32 64
factors of 100=1 2 4 5 10 20 25 50 100
divisors

J[edit]

J has a primitive, q: which returns its argument's prime factors.

q: 40
2 2 2 5

Alternatively, q: can produce provide a table of the exponents of the unique relevant prime factors

   __ q: 420
2 3 5 7
2 1 1 1

With this, we can form lists of each of the potential relevant powers of each of these prime factors

   (^ i.@>:)&.>/ __ q: 420
┌─────┬───┬───┬───┐
1 2 41 31 51 7
└─────┴───┴───┴───┘

From here, it's a simple matter (*/&>@{) to compute all possible factors of the original number

factrs=: */&>@{@((^ i.@>:)&.>/)@q:~&__
factrs 40
1 5
2 10
4 20
8 40

However, a data structure which is organized around the prime decomposition of the argument can be hard to read. So, for reader convenience, we should probably arrange them in a monotonically increasing list:

   factors=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__
factors 420
1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 140 210 420

A less efficient, but concise variation on this theme:

    ~.,*/&> { 1 ,&.> q: 40
1 5 2 10 4 20 8 40

This computes 2^n intermediate values where n is the number of prime factors of the original number.

Another less efficient approach, in which remainders are examined up to the square root, larger factors obtained as fractions, and the combined list nubbed and sorted might be:

factorsOfNumber=: monad define
Y=. y"_
/:~ ~. ( , Y%]) ( #~ 0=]|Y) 1+i.>.%:y
)
 
factorsOfNumber 40
1 2 4 5 8 10 20 40

Another approach:

odometer =: #: i.@(*/)
factors=: (*/@:^"1 odometer@:>:)/@q:~&__

See http://www.jsoftware.com/jwiki/Essays/Odometer

Java[edit]

Works with: Java version 5+
public static TreeSet<Long> factors(long n)
{
TreeSet<Long> factors = new TreeSet<Long>();
factors.add(n);
factors.add(1L);
for(long test = n - 1; test >= Math.sqrt(n); test--)
if(n % test == 0)
{
factors.add(test);
factors.add(n / test);
}
return factors;
}

JavaScript[edit]

Imperative[edit]

function factors(num)
{
var
n_factors = [],
i;
 
for (i = 1; i <= Math.floor(Math.sqrt(num)); i += 1)
if (num % i === 0)
{
n_factors.push(i);
if (num / i !== i)
n_factors.push(num / i);
}
n_factors.sort(function(a, b){return a - b;}); // numeric sort
return n_factors;
}
 
factors(45); // [1,3,5,9,15,45]
factors(53); // [1,53]
factors(64); // [1,2,4,8,16,32,64]

Functional (ES 5)[edit]

Translating the naive list comprehension example from Haskell, using a list monad for the comprehension

// Monadic bind (chain) for lists
function chain(xs, f) {
return [].concat.apply([], xs.map(f));
}
 
// [m..n]
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
return m + i;
});
}
 
function factors_naive(n) {
return chain( range(1, n), function (x) { // monadic chain/bind
return n % x ? [] : [x]; // monadic fail or inject/return
});
}
 
factors_naive(6)

Output:

[1, 2, 3, 6]

Translating the Haskell (lows and highs) example

console.log(
(function (lstTest) {
 
// INTEGER FACTORS
function integerFactors(n) {
var rRoot = Math.sqrt(n),
intRoot = Math.floor(rRoot),
 
lows = range(1, intRoot).filter(function (x) {
return (n % x) === 0;
});
 
// for perfect squares, we can drop the head of the 'highs' list
return lows.concat(lows.map(function (x) {
return n / x;
}).reverse().slice((rRoot === intRoot) | 0));
}
 
// [m .. n]
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
return m + i;
});
}
 
/*************************** TESTING *****************************/
 
// TABULATION OF RESULTS IN SPACED AND ALIGNED COLUMNS
function alignedTable(lstRows, lngPad, fnAligned) {
var lstColWidths = range(0, lstRows.reduce(function (a, x) {
return x.length > a ? x.length : a;
}, 0) - 1).map(function (iCol) {
return lstRows.reduce(function (a, lst) {
var w = lst[iCol] ? lst[iCol].toString().length : 0;
return (w > a) ? w : a;
}, 0);
});
 
return lstRows.map(function (lstRow) {
return lstRow.map(function (v, i) {
return fnAligned(v, lstColWidths[i] + lngPad);
}).join('')
}).join('\n');
}
 
function alignRight(n, lngWidth) {
var s = n.toString();
return Array(lngWidth - s.length + 1).join(' ') + s;
}
 
// TEST
return '\nintegerFactors(n)\n\n' + alignedTable(
lstTest.map(integerFactors).map(function (x, i) {
return [lstTest[i], '-->'].concat(x);
}), 2, alignRight
) + '\n';
 
})([25, 45, 53, 64, 100, 102, 120, 12345, 32766, 32767])
);

Output:

integerFactors(n)
 
25 --> 1 5 25
45 --> 1 3 5 9 15 45
53 --> 1 53
64 --> 1 2 4 8 16 32 64
100 --> 1 2 4 5 10 20 25 50 100
102 --> 1 2 3 6 17 34 51 102
120 --> 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
12345 --> 1 3 5 15 823 2469 4115 12345
32766 --> 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766
32767 --> 1 7 31 151 217 1057 4681 32767
 

jq[edit]

Works with: jq version 1.4
# This implementation uses "sort" for tidiness
def factors:
. as $num
| reduce range(1; 1 + sqrt|floor) as $i
([];
if ($num % $i) == 0 then
($num / $i) as $r
| if $i == $r then . + [$i] else . + [$i, $r] end
else .
end )
| sort;
 
def task:
(45, 53, 64) | "\(.): \(factors)" ;
 
task
Output:
$ jq -n -M -r -c -f factors.jq
45: [1,3,5,9,15,45]
53: [1,53]
64: [1,2,4,8,16,32,64]

Julia[edit]

function factors(n)
f = [one(n)]
for (p,e) in factor(n)
f = reduce(vcat, f, [f*p^j for j in 1:e])
end
return length(f) == 1 ? [one(n), n] : sort!(f)
end
Output:
julia> factors(45)
6-element Array{Int64,1}:
  1
  3
  5
  9
 15
 45

K[edit]

   f:{d:&~x!'!1+_sqrt x;?d,_ x%|d}
 
f 1
1
 
f 3
1 3
 
f 120
1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
 
f 1024
1 2 4 8 16 32 64 128 256 512 1024
 
f 600851475143
1 71 839 1471 6857 59569 104441 486847 1234169 5753023 10086647 87625999 408464633 716151937 8462696833 600851475143
 
#f 3491888400 / has 1920 factors
1920
 
/ Number of factors for 3491888400 .. 3491888409
#:'f' 3491888400+!10
1920 16 4 4 12 16 32 16 8 24

LFE[edit]

Using List Comprehensions[edit]

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

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

Non-Stack-Consuming[edit]

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

 
(defun factors (n)
"Tail-recursive prime factors function."
(factors n 2 '()))
 
(defun factors
((1 _ acc) (++ acc '(1)))
((n _ acc) (when (=< n 0))
#(error undefined))
((n k acc) (when (== 0 (rem n k)))
(factors (div n k) k (cons k acc)))
((n k acc)
(factors n (+ k 1) acc)))
 
Output:
> (factors 10677106534462215678539721403561279)
(104729 104729 104729 98731 98731 32579 29269 1)

Liberty BASIC[edit]

num = 10677106534462215678539721403561279
maxnFactors = 1000
dim primeFactors(maxnFactors), nPrimeFactors(maxnFactors)
global nDifferentPrimeNumbersFound, nFactors, iFactor
 
 
print "Start finding all factors of ";num; ":"
 
nDifferentPrimeNumbersFound=0
dummy = factorize(num,2)
nFactors = showPrimeFactors(num)
dim factors(nFactors)
dummy = generateFactors(1,1)
sort factors(), 0, nFactors-1
for i=1 to nFactors
print i;" ";factors(i-1)
next i
 
print "done"
 
wait
 
 
function factorize(iNum,offset)
factorFound=0
i = offset
do
if (iNum MOD i)=0 _
then
if primeFactors(nDifferentPrimeNumbersFound) = i _
then
nPrimeFactors(nDifferentPrimeNumbersFound) = nPrimeFactors(nDifferentPrimeNumbersFound) + 1
else
nDifferentPrimeNumbersFound = nDifferentPrimeNumbersFound + 1
primeFactors(nDifferentPrimeNumbersFound) = i
nPrimeFactors(nDifferentPrimeNumbersFound) = 1
end if
if iNum/i<>1 then dummy = factorize(iNum/i,i)
factorFound=1
end if
i=i+1
loop while factorFound=0 and i<=sqr(iNum)
if factorFound=0 _
then
nDifferentPrimeNumbersFound = nDifferentPrimeNumbersFound + 1
primeFactors(nDifferentPrimeNumbersFound) = iNum
nPrimeFactors(nDifferentPrimeNumbersFound) = 1
end if
end function
 
 
function showPrimeFactors(iNum)
showPrimeFactors=1
print iNum;" = ";
for i=1 to nDifferentPrimeNumbersFound
print primeFactors(i);"^";nPrimeFactors(i);
if i<nDifferentPrimeNumbersFound then print " * "; else print ""
showPrimeFactors = showPrimeFactors*(nPrimeFactors(i)+1)
next i
end function
 
 
function generateFactors(product,pIndex)
if pIndex>nDifferentPrimeNumbersFound _
then
factors(iFactor) = product
iFactor=iFactor+1
else
for i=0 to nPrimeFactors(pIndex)
dummy = generateFactors(product*primeFactors(pIndex)^i,pIndex+1)
next i
end if
end function
Output:
Start finding all factors of 10677106534462215678539721403561279:
10677106534462215678539721403561279 = 29269^1 * 32579^1 * 98731^2 * 104729^3
1 1
2 29269
3 32579
4 98731
5 104729
6 953554751
7 2889757639
8 3065313101
9 3216557249
10 3411966091
11 9747810361
12 10339998899
13 10968163441
14 94145414120981
15 99864835517479
16 285308661456109
17 302641427774831
18 317573913751019
19 321027175754629
20 336866824130521
21 357331796744339
22 1020878431297169
23 1082897744693371
24 1148684789012489
25 9295070881578575111
26 9859755075476219149
27 10458744358910058191
28 29880090805636839461
29 31695334089430275799
30 33259198413230468851
31 33620855089606540541
32 35279725624365333809
33 37423001741237879131
34 106915577231321212201
35 113410797903992051459
36 973463478356842592799919
37 1032602289299548955255621
38 1095333837964291484285239
39 3129312029983540559911069
40 3319420643851943354153471
41 3483202590619213772296379
42 3694810384914157044482761
43 11197161487859039232598529
44 101949856624833767901342716951
45 108143405156052462534965931709
46 327729719588146219298926345301
47 364792324112959639158827476291
48 10677106534462215678539721403561279
done

[edit]

to factors :n
output filter [equal? 0 modulo :n ?] iseq 1 :n
end
 
show factors 28  ; [1 2 4 7 14 28]

Lua[edit]

function Factors( n ) 
local f = {}
 
for i = 1, n/2 do
if n % i == 0 then
f[#f+1] = i
end
end
f[#f+1] = n
 
return f
end


Maple[edit]

 
numtheory:-divisors(n);
 

Mathematica / Wolfram Language[edit]

Factorize[n_Integer] := Divisors[n]

MATLAB / Octave[edit]

  function fact(n);
f = factor(n); % prime decomposition
K = dec2bin(0:2^length(f)-1)-'0'; % generate all possible permutations
F = ones(1,2^length(f));
for k = 1:size(K)
F(k) = prod(f(~K(k,:))); % and compute products
end;
F = unique(F); % eliminate duplicates
printf('There are %i factors for %i.\n',length(F),n);
disp(F);
end;
 
Output:
>> fact(12)
There are 6 factors for 12.
    1    2    3    4    6   12
>> fact(28)
There are 6 factors for 28.
    1    2    4    7   14   28
>> fact(64)
There are 7 factors for 64.
    1    2    4    8   16   32   64
>>fact(53)
There are 2 factors for 53.
    1   53

Maxima[edit]

The builtin divisors function does this.

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

Such a function could be implemented like so:

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

MAXScript[edit]

 
fn factors n =
(
return (for i = 1 to n+1 where mod n i == 0 collect i)
)
 
Output:
 
factors 3
#(1, 3)
factors 7
#(1, 7)
factors 14
#(1, 2, 7, 14)
factors 60
#(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
factors 54
#(1, 2, 3, 6, 9, 18, 27, 54)
 

Mercury[edit]

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

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

This implementation of factoring works as follows:

  1. The input number itself and 1 are both considered factors.
  2. The numbers between 2 and the square root of the input number are checked for even division.
  3. If the incremental number divides evenly into the input number, both the incremental number and the quotient are added to the list of factors.

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

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

fac.m[edit]

:- module fac.
 
:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.
 
:- implementation.
:- import_module float, int, list, math, string.
 
main(!IO) :-
io.command_line_arguments(Args, !IO),
list.filter_map(string.to_int, Args, CleanArgs),
list.foldl((pred(Arg::in, !.IO::di, !:IO::uo) is det :-
factor(Arg, X),
io.format("factor(%d, [", [i(Arg)], !IO),
io.write_list(X, ",", io.write_int, !IO),
io.write_string("])\n", !IO)
), CleanArgs, !IO).
 
:- pred factor(int::in, list(int)::out) is det.
factor(N, Factors) :-
Limit = float.truncate_to_int(math.sqrt(float(N))),
factor(N, 2, Limit, [], Unsorted),
list.sort_and_remove_dups([1, N | Unsorted], Factors).
 
:- pred factor(int, int, int, list(int), list(int)).
:- mode factor(in, in, in, in, out) is det.
factor(N, X, Limit, !Accumulator) :-
( if X > Limit
then true
else ( if 0 = N mod X
then !:Accumulator = [X, N / X | !.Accumulator]
else true ),
factor(N, X + 1, Limit, !Accumulator) ).
 
:- func factor(int) = list(int).
%:- mode factor(in) = out is det.
factor(N) = Factors :- factor(N, Factors).
 
:- end_module fac.

Use and output[edit]

Use of the code looks like this:

$ mmc fac.m && ./fac 100 999 12345678 booger
factor(100, [1,2,4,5,10,20,25,50,100])
factor(999, [1,3,9,27,37,111,333,999])
factor(12345678, [1,2,3,6,9,18,47,94,141,282,423,846,14593,29186,43779,87558,131337,262674,685871,1371742,2057613,4115226,6172839,12345678])

МК-61/52[edit]

П9	1	П6	КИП6	ИП9	ИП6	/	П8	^	[x]
x#0	21	-	x=0	03	ИП6	С/П	ИП8	П9	БП
04	1	С/П	БП	21

MUMPS[edit]

factors(num)	New fctr,list,sep,sqrt
If num<1 Quit "Too small a number"
If num["." Quit "Not an integer"
Set sqrt=num**0.5\1
For fctr=1:1:sqrt Set:num/fctr'["." list(fctr)=1,list(num/fctr)=1
Set (list,fctr)="",sep="[" For Set fctr=$Order(list(fctr)) Quit:fctr="" Set list=list_sep_fctr,sep=","
Quit list_"]"
 
w $$factors(45) ; [1,3,5,9,15,45]
w $$factors(53) ; [1,53]
w $$factors(64) ; [1,2,4,8,16,32,64]

NetRexx[edit]

Translation of: REXX
/* NetRexx ***********************************************************
* 21.04.2013 Walter Pachl
* 21.04.2013 add method main to accept argument(s)
*********************************************************************/

options replace format comments java crossref symbols nobinary
class divl
method main(argwords=String[]) static
arg=Rexx(argwords)
Parse arg a b
Say a b
If a='' Then Do
help='java divl low [high] shows'
help=help||' divisors of all numbers between low and high'
Say help
Return
End
If b='' Then b=a
loop x=a To b
say x '->' divs(x)
End
 
method divs(x) public static returns Rexx
if x==1 then return 1 /*handle special case of 1 */
lo=1
hi=x
odd=x//2 /* 1 if x is odd */
loop j=2+odd By 1+odd While j*j<x /*divide by numbers<sqrt(x) */
if x//j==0 then Do /*Divisible? Add two divisors:*/
lo=lo j /* list low divisors */
hi=x%j hi /* list high divisors */
End
End
If j*j=x Then /*for a square number as input */
lo=lo j /* add its square root */
return lo hi /* return both lists */
Output:
java divl 1 10
1 -> 1
2 -> 1 2
3 -> 1 3
4 -> 1 2 4
5 -> 1 5
6 -> 1 2 3 6
7 -> 1 7
8 -> 1 2 4 8
9 -> 1 3 9
10 -> 1 2 5 10

Nim[edit]

import intsets, math, algorithm
 
proc factors(n): seq[int] =
var fs = initIntSet()
for x in 1 .. int(sqrt(float(n))):
if n mod x == 0:
fs.incl(x)
fs.incl(n div x)
 
result = @[]
for x in fs:
result.add(x)
sort(result, system.cmp[int])
 
echo factors(45)

Niue[edit]

[ 'n ; [ negative-or-zero [ , ] if 
[ n not-factor [ , ] when ] else ] n times n ] 'factors ;
 
[ dup 0 <= ] 'negative-or-zero ;
[ swap dup rot swap mod 0 = not ] 'not-factor ;
 
( tests )
100 factors .s .clr ( => 1 2 4 5 10 20 25 50 100 ) newline
53 factors .s .clr ( => 1 53 ) newline
64 factors .s .clr ( => 1 2 4 8 16 32 64 ) newline
12 factors .s .clr ( => 1 2 3 4 6 12 )

Oberon-2[edit]

Oxford Oberon-2

 
MODULE Factors;
IMPORT Out,SYSTEM;
TYPE
LIPool = POINTER TO ARRAY OF LONGINT;
LIVector= POINTER TO LIVectorDesc;
LIVectorDesc = RECORD
cap: INTEGER;
len: INTEGER;
LIPool: LIPool;
END;
 
PROCEDURE New(cap: INTEGER): LIVector;
VAR
v: LIVector;
BEGIN
NEW(v);
v.cap := cap;
v.len := 0;
NEW(v.LIPool,cap);
RETURN v
END New;
 
PROCEDURE (v: LIVector) Add(x: LONGINT);
VAR
newLIPool: LIPool;
BEGIN
IF v.len = LEN(v.LIPool^) THEN
(* run out of space *)
v.cap := v.cap + (v.cap DIV 2);
NEW(newLIPool,v.cap);
SYSTEM.MOVE(SYSTEM.ADR(v.LIPool^),SYSTEM.ADR(newLIPool^),v.cap * SIZE(LONGINT));
v.LIPool := newLIPool
END;
v.LIPool[v.len] := x;
INC(v.len)
END Add;
 
PROCEDURE (v: LIVector) At(idx: INTEGER): LONGINT;
BEGIN
RETURN v.LIPool[idx];
END At;
 
 
PROCEDURE Factors(n:LONGINT): LIVector;
VAR
j: LONGINT;
v: LIVector;
BEGIN
v := New(16);
FOR j := 1 TO n DO
IF (n MOD j) = 0 THEN v.Add(j) END;
END;
RETURN v
END Factors;
 
VAR
v: LIVector;
j: INTEGER;
BEGIN
v := Factors(123);
FOR j := 0 TO v.len - 1 DO
Out.LongInt(v.At(j),4);Out.Ln
END;
Out.Int(v.len,6);Out.String(" factors");Out.Ln
END Factors.
 
Output:
   
   1
   3
  41
 123
     4 factors

Objeck[edit]

use IO;
use Structure;
 
bundle Default {
class Basic {
function : native : GenerateFactors(n : Int) ~ IntVector {
factors := IntVector->New();
factors-> AddBack(1);
factors->AddBack(n);
 
for(i := 2; i * i <= n; i += 1;) {
if(n % i = 0) {
factors->AddBack(i);
if(i * i <> n) {
factors->AddBack(n / i);
};
};
};
factors->Sort();
 
 
return factors;
}
 
function : Main(args : String[]) ~ Nil {
numbers := [3135, 45, 60, 81];
for(i := 0; i < numbers->Size(); i += 1;) {
factors := GenerateFactors(numbers[i]);
 
Console->GetInstance()->Print("Factors of ")->Print(numbers[i])->PrintLine(" are:");
each(i : factors) {
Console->GetInstance()->Print(factors->Get(i))->Print(", ");
};
"\n\n"->Print();
};
}
}
}

OCaml[edit]

let rec range = function 0 -> [] | n -> range(n-1) @ [n]
 
let factors n =
List.filter (fun v -> (n mod v) = 0) (range n)

Oforth[edit]

Integer method: factors { self seq filter(#[ self isMultiple ]) }
 
120 factors println
Output:
[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]

Oz[edit]

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

PARI/GP[edit]

divisors(n)

Panda[edit]

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

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

Pascal[edit]

Translation of: Fortran
Works with: Free Pascal version 2.6.2
program Factors;
var
i, number: integer;
begin
write('Enter a number between 1 and 2147483647: ');
readln(number);
 
for i := 1 to round(sqrt(number)) - 1 do
if number mod i = 0 then
write (i, ' ', number div i, ' ');
 
// Check to see if number is a square
i := round(sqrt(number));
if i*i = number then
write(i)
else if number mod i = 0 then
write(i, number/i);
writeln;
end.
Output:
Enter a number between 1 and 2147483647: 49
1 49 7

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

small improvement[edit]

the factors are in ascending order.

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

 
const
MAXFACTORCNT = 1920; //number := 3491888400;
 
var
FaktorList : array[0..MAXFACTORCNT] of LongWord;
i, number,quot,cnt: LongWord;
begin
writeln('Enter a number between 1 and 4294967295: ');
write('3491888400 is a nice choice ');
readln(number);
 
cnt := 0;
i := 1;
repeat
quot := number div i;
if quot *i-number = 0 then
begin
FaktorList[cnt] := i;
FaktorList[MAXFACTORCNT-cnt] := quot;
inc(cnt);
end;
inc(i);
until i> quot;
writeln(number,' has ',2*cnt,' factors');
dec(cnt);
For i := 0 to cnt do
write(FaktorList[i],' ,');
For i := cnt downto 1 do
write(FaktorList[MAXFACTORCNT-i],' ,');
{ the last without ','}
writeln(FaktorList[MAXFACTORCNT]);
end.
Output:
Enter a number between 1 and 4294967295: 
3491888400 is a nice choice 120
120 has 16 factors
1 ,2 ,3 ,4 ,5 ,6 ,8 ,10 ,12 ,15 ,20 ,24 ,30 ,40 ,60 ,120

Perl[edit]

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

Or more intelligently:

sub factors {
my $n = shift;
$n = -$n if $n < 0;
my @divisors;
for (1 .. int(sqrt($n))) { # faster and less memory than map/grep
push @divisors, $_ unless $n % $_;
}
# Return divisors including top half, without duplicating a square
@divisors, map { $_*$_ == $n ? () : int($n/$_) } reverse @divisors;
}
print join " ", factors(64), "\n";

One could also use a module, e.g.:

Library: ntheory
use ntheory qw/divisors/;
print join " ", divisors(12345678), "\n";
# Alternately something like: fordivisors { say } 12345678;

Perl 6[edit]

Works with: Rakudo version 2015.12
sub factors (Int $n) { squish sort ($_, $n div $_ if $n %% $_ for 1 .. sqrt $n) }

Phix[edit]

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

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

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

PHP[edit]

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

PicoLisp[edit]

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

PL/I[edit]

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

PowerShell[edit]

Straightforward but slow[edit]

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

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

A little more clever[edit]

function Get-Factor ($a) {
1..[Math]::Sqrt($a) `
| Where-Object { $a % $_ -eq 0 } `
| ForEach-Object { $_; $a / $_ } `
| Sort-Object -Unique
}

Here the range of integers is only taken up to the square root of the number, the same filtering applies. Afterwards the corresponding larger factors are calculated and sent down the pipeline along with the small ones found earlier.

ProDOS[edit]

Uses the math module:

editvar /newvar /value=a /userinput=1 /title=Enter an integer:
do /delimspaces %% -a- >b
printline Factors of -a-: -b-

Prolog[edit]

Simple Brute Force Implementation

 
brute_force_factors( N , Fs ) :-
integer(N) ,
N > 0 ,
setof( F , ( between(1,N,F) , N mod F =:= 0 ) , Fs )
.
 

A Slightly Smarter Implementation

 
smart_factors(N,Fs) :-
integer(N) ,
N > 0 ,
setof( F , factor(N,F) , Fs )
.
 
factor(N,F) :-
L is floor(sqrt(N)) ,
between(1,L,X) ,
0 =:= N mod X ,
( F = X ; F is N // X )
.
 

Not every Prolog has between/3: you might need this:

 
 
between(X,Y,Z) :-
integer(X) ,
integer(Y) ,
X =< Z ,
between1(X,Y,Z)
.
 
between1(X,Y,X) :-
X =< Y
.
between1(X,Y,Z) :-
X < Y ,
X1 is X+1 ,
between1(X1,Y,Z)
.
 
Output:
?- N=36 ,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ).
N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] ;
N = 36, Factors = [1, 2, 3, 4, 6, 9, 12, 18, 36] .

?- N=53,( brute_force_factors(N,Factors) ; smart_factors(N,Factors) ).
N = 53, Factors = [1, 53] ;
N = 53, Factors = [1, 53] .

?- N=100,( brute_force_factors(N,Factors);smart_factors(N,Factors) ).
N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] ;
N = 100, Factors = [1, 2, 4, 5, 10, 20, 25, 50, 100] .

?- N=144,( brute_force_factors(N,Factors);smart_factors(N,Factors) ).
N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] ;
N = 144, Factors = [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144] .

?- N=32765,( brute_force_factors(N,Factors);smart_factors(N,Factors) ).
N = 32765, Factors = [1, 5, 6553, 32765] ;
N = 32765, Factors = [1, 5, 6553, 32765] .

?- N=32766,( brute_force_factors(N,Factors);smart_factors(N,Factors) ).
N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] ;
N = 32766, Factors = [1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766] .

38 ?- N=32767,( brute_force_factors(N,Factors);smart_factors(N,Factors) ).
N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] ;
N = 32767, Factors = [1, 7, 31, 151, 217, 1057, 4681, 32767] .

PureBasic[edit]

Procedure PrintFactors(n)
Protected i, lim=Round(sqr(n),#PB_Round_Up)
NewList F.i()
For i=1 To lim
If n%i=0
AddElement(F()): F()=i
AddElement(F()): F()=n/i
EndIf
Next
;- Present the result
SortList(F(),#PB_Sort_Ascending)
ForEach F()
Print(str(F())+" ")
Next
EndProcedure
 
If OpenConsole()
Print("Enter integer to factorize: ")
PrintFactors(Val(Input()))
Print(#CRLF$+#CRLF$+"Press ENTER to quit."): Input()
EndIf
Output:
 Enter integer to factorize: 96
 1 2 3 4 6 8 12 16 24 32 48 96

Python[edit]

Naive and slow but simplest (check all numbers from 1 to n):

>>> def factors(n):
return [i for i in range(1, n + 1) if not n%i]

Slightly better (realize that there are no factors between n/2 and n):

>>> def factors(n):
return [i for i in range(1, n//2 + 1) if not n%i] + [n]
 
>>> factors(45)
[1, 3, 5, 9, 15, 45]

Much better (realize that factors come in pairs, the smaller of which is no bigger than sqrt(n)):

>>> from math import sqrt
>>> def factor(n):
factors = set()
for x in range(1, int(sqrt(n)) + 1):
if n % x == 0:
factors.add(x)
factors.add(n//x)
return sorted(factors)
 
>>> for i in (45, 53, 64): print( "%i: factors: %s" % (i, factor(i)) )
 
45: factors: [1, 3, 5, 9, 15, 45]
53: factors: [1, 53]
64: factors: [1, 2, 4, 8, 16, 32, 64]

More efficient when factoring many numbers:

from itertools import chain, cycle, accumulate # last of which is Python 3 only
 
def factors(n):
def prime_powers(n):
# c goes through 2, 3, 5, then the infinite (6n+1, 6n+5) series
for c in accumulate(chain([2, 1, 2], cycle([2,4]))):
if c*c > n: break
if n%c: continue
d,p = (), c
while not n%c:
n,p,d = n//c, p*c, d + (p,)
yield(d)
if n > 1: yield((n,))
 
r = [1]
for e in prime_powers(n):
r += [a*b for a in r for b in e]
return r

R[edit]

factors <- function(n)
{
if(length(n) > 1)
{
lapply(as.list(n), factors)
} else
{
one.to.n <- seq_len(n)
one.to.n[(n %% one.to.n) == 0]
}
}
factors(60)
1  2  3  4  5  6 10 12 15 20 30 60
factors(c(45, 53, 64))
[[1]]
[1]  1  3  5  9 15 45
[[2]]
[1]  1 53
[[3]]
[1]  1  2  4  8 16 32 64

Racket[edit]

 
#lang racket
 
;; a naive version
(define (naive-factors n)
(for/list ([i (in-range 1 (add1 n))] #:when (zero? (modulo n i))) i))
(naive-factors 120) ; -> '(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120)
 
;; much better: use `factorize' to get prime factors and construct the
;; list of results from that
(require math)
(define (factors n)
(sort (for/fold ([l '(1)]) ([p (factorize n)])
(append (for*/list ([e (in-range 1 (add1 (cadr p)))] [x l])
(* x (expt (car p) e)))
l))
<))
(naive-factors 120) ; -> same
 
;; to see how fast it is:
(define huge 1200034005600070000008900000000000000000)
(time (length (factors huge)))
;; I get 42ms for getting a list of 7776 numbers
 
;; but actually the math library comes with a `divisors' function that
;; does the same, except even faster
(divisors 120) ; -> same
 
(time (length (divisors huge)))
;; And this one clocks at 17ms
 

REALbasic[edit]

Function factors(num As UInt64) As UInt64()
'This function accepts an unsigned 64 bit integer as input and returns an array of unsigned 64 bit integers
Dim result() As UInt64
Dim iFactor As UInt64 = 1
While iFactor <= num/2 'Since a factor will never be larger than half of the number
If num Mod iFactor = 0 Then
result.Append(iFactor)
End If
iFactor = iFactor + 1
Wend
result.Append(num) 'Since a given number is always a factor of itself
Return result
End Function

REXX[edit]

optimized version[edit]

This REXX version has no effective limits on the number of decimal digits in the number to be factored   [by adjusting the number of digits (precision)].
This REXX version also supports negative integers and zero.
It also indicates   primes   in the output as well as the number of factors.

/*REXX program displays divisors of any  [negative/zero/positive]  integer(s).*/
parse arg bot top inc . /*optional args.*/
top=word(top bot 20,1); bot=word(bot 1,1); inc=word(inc 1,1) /*range options.*/
w=length(high)+1; numeric digits max(9,w); $='∞' /*digits for // */
@.=left('',7); @.1='{unity}'; @.2='[prime]'; @.$=' {'$"} " /*some literals.*/
say center('n',1+w) '#divisors' center('divisors',60) /*show a header.*/
say copies('═',1+w) '═════════' copies('═' ,60) /* " " sep. */
 
do n=bot to top by inc; divs=divisors(n); #=words(divs)
if divs==$ then do; #=$; divs=' (infinite)'; end /*handle infinity*/
p=@.#; if n<0 then p=@.. /*handle negative*/
say center(n,w+1) center('['#"]",9) "──► " p ' ' divs
end /*n*/ /* [↑] process a range of integers. */
exit /*stick a fork in it, we're all done. */
/*────────────────────────────────────────────────────────────────────────────*/
divisors: procedure; parse arg x; x=abs(x); if x==1 then return 1
odd=x//2; b=x; if x==0 then return '∞'
a=1 /* [↓] process only EVEN│ODD integers.*/
do j=2+odd by 1+odd while j*j<x /*divide by all integers up to √x. */
if x//j==0 then do; a=a j; b=x%j b; end /*÷? Add factors to α&ß lists.*/
end /*j*/ /* [↑]  % is REXX's integer division.*/
/* [↓] adjust for a square. ___ */
if j*j==x then return a j b /*Was X a square? If so, insert √ x */
return a b /*return the divisors of both lists. */

output   when the input used is:   -6  200

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

Alternate Version[edit]

/* REXX ***************************************************************
* Program to calculate and show divisors of positive integer(s).
* 03.08.2012 Walter Pachl simplified the above somewhat
* in particular I see no benefit from divAdd procedure
* 04.08.2012 the reference to 'above' is no longer valid since that
* was meanwhile changed for the better.
* 04.08.2012 took over some improvements from new above
**********************************************************************/

Parse arg low high .
Select
When low='' Then Parse Value '1 200' with low high
When high='' Then high=low
Otherwise Nop
End
do j=low to high
say ' n = ' right(j,6) " divisors = " divs(j)
end
exit
 
divs: procedure; parse arg x
if x==1 then return 1 /*handle special case of 1 */
Parse Value '1' x With lo hi /*initialize lists: lo=1 hi=x */
odd=x//2 /* 1 if x is odd */
Do j=2+odd By 1+odd While j*j<x /*divide by numbers<sqrt(x) */
if x//j==0 then Do /*Divisible? Add two divisors:*/
lo=lo j /* list low divisors */
hi=x%j hi /* list high divisors */
End
End
If j*j=x Then /*for a square number as input */
lo=lo j /* add its square root */
return lo hi /* return both lists */

Ruby[edit]

class Integer
def factors() (1..self).select { |n| (self % n).zero? } end
end
p 45.factors
[1, 3, 5, 9, 15, 45]

As we only have to loop up to , we can write

class Integer
def factors
1.upto(Math.sqrt(self)).select {|i| (self % i).zero?}.inject([]) do |f, i|
f << self/i unless i == self/i
f << i
end.sort
end
end
[45, 53, 64].each {|n| puts "#{n} : #{n.factors}"}
Output:
45 : [1, 3, 5, 9, 15, 45]
53 : [1, 53]
64 : [1, 2, 4, 8, 16, 32, 64]

Run BASIC[edit]

PRINT "Factors of 45 are ";factorlist$(45)
PRINT "Factors of 12345 are "; factorlist$(12345)
END
 
function factorlist$(f)
DIM L(100)
FOR i = 1 TO SQR(f)
IF (f MOD i) = 0 THEN
L(c) = i
c = c + 1
IF (f <> i^2) THEN
L(c) = (f / i)
c = c + 1
END IF
END IF
NEXT i
s = 1
while s = 1
s = 0
for i = 0 to c-1
if L(i) > L(i+1) and L(i+1) <> 0 then
t = L(i)
L(i) = L(i+1)
L(i+1) = t
s = 1
end if
next i
wend
FOR i = 0 TO c-1
factorlist$ = factorlist$ + STR$(L(i)) + ", "
NEXT
end function
Output:
Factors of 45 are 1, 3, 5, 9, 15, 45, 
Factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, 12345, 

Sather[edit]

Translation of: C++
class MAIN is
 
factors(n :INT):ARRAY{INT} is
f:ARRAY{INT};
f := #;
f := f.append(|1|);
f := f.append(|n|);
loop i ::= 2.upto!( n.flt.sqrt.int );
if n%i = 0 then
f := f.append(|i|);
if (i*i) /= n then f := f.append(|n / i|); end;
end;
end;
f.sort;
return f;
end;
 
main is
a :ARRAY{INT} := |3135, 45, 64, 53, 45, 81|;
loop l ::= a.elt!;
#OUT + "factors of " + l + ": ";
r ::= factors(l);
loop ri ::= r.elt!;
#OUT + ri + " ";
end;
#OUT + "\n";
end;
end;
end;

Scala[edit]

 
def factors(num: Int) = {
(1 to num).filter { divisor =>
num % divisor == 0
}
}

Scheme[edit]

This implementation uses a naive trial division algorithm.

(define (factors n)
(define (*factors d)
(cond ((> d n) (list))
((= (modulo n d) 0) (cons d (*factors (+ d 1))))
(else (*factors (+ d 1)))))
(*factors 1))
 
(display (factors 1111111))
(newline)
Output:
 (1 239 4649 1111111)

Seed7[edit]

$ include "seed7_05.s7i";
 
const proc: writeFactors (in integer: number) is func
local
var integer: testNum is 0;
begin
write("Factors of " <& number <& ": ");
for testNum range 1 to sqrt(number) do
if number rem testNum = 0 then
if testNum <> 1 then
write(", ");
end if;
write(testNum);
if testNum <> number div testNum then
write(", " <& number div testNum);
end if;
end if;
end for;
writeln;
end func;
 
const proc: main is func
local
const array integer: numsToFactor is [] (45, 53, 64);
var integer: number is 0;
begin
for number range numsToFactor do
writeFactors(number);
end for;
end func;
Output:
Factors of 45: 1, 45, 3, 15, 5, 9
Factors of 53: 1, 53
Factors of 64: 1, 64, 2, 32, 4, 16, 8

SequenceL[edit]

Brute Force Method

A simple brute force method using an indexed partial function as a filter.

Factors(num(0))[i] := i when num mod i = 0 foreach i within 1 ... num;

Slightly More Efficient Method

A slightly more efficient method, only going up to the sqrt(n).

Factors(num(0)) :=
let
factorPairs[i] :=
[i] when i = sqrt(num)
else
[i, num/i] when num mod i = 0
foreach i within 1 ... floor(sqrt(num));
in
join(factorPairs);

Sidef[edit]

func factors(n) {
var divs = []
range(1, n.sqrt.int).each { |d|
divs << d if n%%d
}
divs + [divs[-1]**2 == n ? divs.pop : ()] + divs.reverse.map{|d| n/d }
}
 
[53, 64, 32766].each { |n|
say "factors(#{n}): #{factors(n)}"
}
Output:
factors(53): 1 53
factors(64): 1 2 4 8 16 32 64
factors(32766): 1 2 3 6 43 86 127 129 254 258 381 762 5461 10922 16383 32766

Slate[edit]

n@(Integer traits) primeFactors
[
[| :result |
result nextPut: 1.
n primesDo: [| :prime | result nextPut: prime]] writingAs: {}
].

where primesDo: is a part of the standard numerics library:

n@(Integer traits) primesDo: block
"Decomposes the Integer into primes, applying the block to each (in increasing
order)."
[| div next remaining |
div: 2.
next: 3.
remaining: n.
[[(remaining \\ div) isZero]
whileTrue:
[block applyTo: {div}.
remaining: remaining // div].
remaining = 1] whileFalse:
[div: next.
next: next + 2] "Just looks at the next odd integer."
].

Smalltalk[edit]

Copied from the Python example, but code added to the Integer built in class:

Integer>>factors
| a |
a := OrderedCollection new.
1 to: (self / 2) do: [ :i |
((self \\ i) = 0) ifTrue: [ a add: i ] ].
a add: self.
^a

Then use as follows:

 
59 factors -> an OrderedCollection(1 59)
120 factors -> an OrderedCollection(1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120)
 

Swift[edit]

Simple implementation:

func factors(n: Int) -> [Int] {
 
return filter(1...n) { n % $0 == 0 }
}

More efficient implementation:

import func Darwin.sqrt
 
func sqrt(x:Int) -> Int { return Int(sqrt(Double(x))) }
 
func factors(n: Int) -> [Int] {
 
var result = [Int]()
 
for factor in filter (1...sqrt(n), { n % $0 == 0 }) {
 
result.append(factor)
 
if n/factor != factor { result.append(n/factor) }
}
 
return sorted(result)
 
}

Call:

println(factors(4))
println(factors(1))
println(factors(25))
println(factors(63))
println(factors(19))
println(factors(768))
Output:
[1, 2, 4]
[1]
[1, 5, 25]
[1, 3, 7, 9, 21, 63]
[1, 19]
[1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768]

Tcl[edit]

proc factors {n} {
set factors {}
for {set i 1} {$i <= sqrt($n)} {incr i} {
if {$n % $i == 0} {
lappend factors $i [expr {$n / $i}]
}
}
return [lsort -unique -integer $factors]
}
puts [factors 64]
puts [factors 45]
puts [factors 53]
Output:
1 2 4 8 16 32 64
1 3 5 9 15 45
1 53

UNIX Shell[edit]

This should work in all Bourne-compatible shells, assuming the system has both sort and at least one of bc or dc.

factor() {
r=`echo "sqrt($1)" | bc` # or `echo $1 v p | dc`
i=1
while [ $i -lt $r ]; do
if [ `expr $1 % $i` -eq 0 ]; then
echo $i
expr $1 / $i
fi
i=`expr $i + 1`
done | sort -nu
}
 

Ursala[edit]

The simple way:

#import std
#import nat
 
factors "n" = (filter not remainder/"n") nrange(1,"n")

The complicated way:

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

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

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

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

#cast %nL
 
example = factors 100
Output:
<1,2,4,5,10,20,25,50,100>

VBA[edit]

Function Factors(x As Integer) As String
Application.Volatile
Dim i As Integer
Dim cooresponding_factors As String
Factors = 1
corresponding_factors = x
For i = 2 To Sqr(x)
If x Mod i = 0 Then
Factors = Factors & ", " & i
If i <> x / i Then corresponding_factors = x / i & ", " & corresponding_factors
End If
Next i
If x <> 1 Then Factors = Factors & ", " & corresponding_factors
End Function
Output:
cell formula is "=Factors(840)"
resultant value is "1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840"

Wortel[edit]

@let {
factors1 &n !-\%%n @to n
factors_tacit @(\\%% !- @to)
[[
 !factors1 10
 !factors_tacit 100
 !factors1 720
]]
}
Returns:
[
  [1 2 5 10]
  [1 2 4 5 10 20 25 50 100]
  [1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 40 45 48 60 72 80 90 120 144 180 240 360 720]
]

XPL0[edit]

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;
]
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[edit]

Translation of: Chapel
fcn f(n){ (1).pump(n.toFloat().sqrt(), List,
'wrap(m){((n % m)==0) and T(m,n/m) or Void.Skip}) }
fcn g(n){ [[(m); [1..n.toFloat().sqrt()],'{n%m==0}; '{T(m,n/m)} ]] } // list comprehension
Output:
zkl: f(45)
L(L(1,45),L(3,15),L(5,9))

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