Factors of an integer
From Rosetta Code
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:
Compute the factors of a number. The factors of a positive integer are those positive integers by which it 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 is 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 even prime numbers will have at least two factors; ‘1’ and themselves.
See also:
[edit] ActionScript
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;
}
[edit] Aikido
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))
[edit] ALGOL 68
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
[edit] AutoHotkey
msgbox, % factors(45) "`n" factors(53) "`n" factors(64)
Factors(n)
{ Loop, % floor(sqrt(n))
{ v := A_Index = 1 ? 1 "," n : mod(n,A_Index) ? v : v "," A_Index "," n//A_Index
}
Sort, v, N U D,
Return, v
}
Output: 1,3,5,9,15,45 1,53 1,2,4,8,16,32,64
[edit] Batch File
Command line version:
@echo off
set res=Factors of %1:
for /L %%i in (1,1,%1) do call :fac %1 %%i
echo %res%
goto :eof
:fac
set /a test = %1 %% %2
if %test% equ 0 set res=%res% %2
Outputs:
>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
Outputs:
>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
[edit] BASIC
Works with: QBasic
This example stores the factors in a shared array (with the original number as the last element) for later retrieval.
Note that this will error out if you pass 32767 (or higher).
DECLARE SUB factor (what AS INTEGER)
REDIM SHARED factors(0) AS INTEGER
DIM i AS INTEGER, L AS INTEGER
INPUT "Gimme a number"; i
factor i
PRINT factors(0);
FOR L = 1 TO UBOUND(factors)
PRINT ","; factors(L);
NEXT
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
Sample outputs:
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
[edit] C
#include <stdio.h>
#include <stdlib.h>
typedef struct {
int *list;
short count;
} Factors;
void xferFactors( Factors *fctrs, int *flist, int flix )
{
int ix, ij;
int newSize = fctrs->count + flix;
if (newSize > flix) {
fctrs->list = realloc( fctrs->list, newSize * sizeof(int));
}
else {
fctrs->list = malloc( newSize * sizeof(int));
}
for (ij=0,ix=fctrs->count; ix<newSize; ij++,ix++) {
fctrs->list[ix] = flist[ij];
}
fctrs->count = newSize;
}
Factors *factor( int num, Factors *fctrs)
{
int flist[301], flix;
int dvsr;
flix = 0;
fctrs->count = 0;
if (fctrs->list) 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;
}
[edit] C++
#include <iostream>
#include <vector>
#include <algorithm>
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;
}
}
[edit] C#
C# 3.0
using System;
using System.Linq;
using System.Collections.Generic;
public static class Extension
{
public static List<int> Factors(this int me)
{
return Enumerable.Range(1, me).Where(x => me % x == 0).ToList();
}
}
class Program
{
static void Main(string[] args)
{
Console.WriteLine(String.Join(", ", 45.Factors()));
}
}
C# 1.0
static void Main(string[] args)
{
do
{
Console.WriteLine("Number:");
Int64 p = 0;
do
{
try
{
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);
}
Example output:
Number: 32434243 For 1 through 5695 Found: 1. 32434243 / 1 = 32434243 Found: 307. 32434243 / 307 = 105649 Done.
[edit] Clojure
(defn factors [n]
(filter #(zero? (rem n %)) (range 1 (inc n))))
(print (factors 45))
(1 3 5 9 15 45)
Improved version. Considers small factors from 1 up to (sqrt n) -- we increment it because range does not include the end point. Pair each small factor with its co-factor, flattening the results, and put them into a sorted set to get the factors in order.
(defn factors [n]
(into (sorted-set)
(mapcat (fn [x] [x (/ n x)])
(filter #(zero? (rem n %)) (range 1 (inc (sqrt n)))) )))
Same idea, using for comprehensions.
(defn factors [n]
(into (sorted-set)
(reduce concat
(for [x (range 1 (inc (sqrt n))) :when (zero? (rem n x))]
[x (/ n x)]))))
[edit] Common Lisp
We iterate in the range 1..sqrt(n) collecting ‘low’ factors and corresponding ‘high’ factors, and combine at the end to produce an ordered list of factors.
(defun factors (n &aux (lows '()) (highs '()))
(do ((limit (isqrt n)) (factor 1 (1+ factor)))
((= factor limit)
(when (= n (* limit limit))
(push limit highs))
(nreconc lows highs))
(multiple-value-bind (quotient remainder) (floor n factor)
(when (zerop remainder)
(push factor lows)
(push quotient highs)))))
[edit] D
import std.stdio ;
T[] factor(T)(T n) {
bool[T] result ;
for(T i = 1 ; i*i <= n ; i++)
if (n % i == 0) {
result[i] = true ;
result[n/i] = true ;
}
return result.keys.sort ;
}
void main() {
foreach(i ; [45, 53, 64, 1111111])
writefln("%s", factor(i)) ;
}
[edit] E
def factors(x :(int > 0)) {
var xfactors := []
for f ? (x % f <=> 0) in 1..x {
xfactors with= f
}
return xfactors
}
[edit] Erlang
factors(N) ->
[I || I <- lists:seq(1,N div 2), N rem I == 0]++[N].
[edit] F#
let factors n = [for i in 1..n do if n%i=0 then yield i]
[edit] Factor
USE: math.primes.factors
( scratchpad ) 24 divisors .
{ 1 2 3 4 6 8 12 24 }
[edit] FALSE
[1[\$@$@-][\$@$@$@$@\/*=[$." "]?1+]#.%]f:
45f;! 53f;! 64f;!
[edit] Forth
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
[edit] Haskell
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
[edit] HicEst
DLG(NameEdit=N, TItle='Enter an integer')
DO i = 1, N^0.5
IF( MOD(N,i) == 0) WRITE() i, N/i
ENDDO
END
[edit] Icon and Unicon
[edit] Icon
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
Sample 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
The Library: Icon Programming Library divisors
[edit] Unicon
The Icon solution works in Unicon.
[edit] J
J has a primitive, q: which returns its 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: 40
2 5
3 1
With this, we can form lists of each of the potential relevant powers of each of these prime factors
((^ i.@>:)&.>/) __ q: 40
┌───────┬───┐ │1 2 4 8│1 5│ └───────┴───┘
From here, it's a simple matter to compute all possible factors of the original number
factors=: */&>@{@((^ i.@>:)&.>/)@q:~&__
factors 40
1 5
2 10
4 20
8 40
A 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:
factors=: monad define
Y=. y"_
/:~ ~. ( , Y%]) ( #~ 0=]|Y) 1+i.>.%:y
)
factors 40
1 2 4 5 8 10 20 40
[edit] Java
Works with: Java version 1.5+
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;
}
[edit] JavaScript
function factors(num) {
var factors = new Array();
var sqrt = Math.floor(Math.sqrt(num));
for (var i = 1; i <= sqrt; i++) {
if (num % i == 0) {
factors.push(i);
if (num / i != i)
factors.push(num / i);
}
}
factors.sort(function(a,b){return a-b}); // numeric sort
return factors;
}
factors(45); // [1,3,5,9,15,45]
factors(53); // [1,53]
factors(64); // [1,2,4,8,16,32,64]
[edit] Logo
to factors :n
output filter [equal? 0 modulo :n ?] iseq 1 :n
end
show factors 28 ; [1 2 4 7 14 28]
[edit] Mathematica
Factorize[n_Integer] := Divisors[n]
[edit] Maxima
The builtin divisors function does this.
(%i96) divisors(100);
(%o96) {1,2,4,5,10,20,25,50,100}
Such a function could be implemented like so:
divisors2(n) := map( lambda([l], lreduce("*", l)),
apply( cartesian_product,
map( lambda([fac],
setify(makelist(fac[1]^i, i, 0, fac[2]))),
ifactors(n))));
[edit] MUMPS
factors(num) New fctr,list,sep,sqrt
If num<1 Quit "Too small a number"
If num["." Quit "Not an integer"
Set sqrt=num**0.5\1
For fctr=1:1:sqrt Set:num/fctr'["." list(fctr)=1,list(num/fctr)=1
Set (list,fctr)="",sep="[" For Set fctr=$Order(list(fctr)) Quit:fctr="" Set list=list_sep_fctr,sep=","
Quit list_"]"
w $$factors(45) ; [1,3,5,9,15,45]
w $$factors(53) ; [1,53]
w $$factors(64) ; [1,2,4,8,16,32,64]
[edit] Niue
[ 'n ; [ negative-or-zero [ , ] if
[ n not-factor [ , ] when ] else ] n times n ] 'factors ;
[ dup 0 <= ] 'negative-or-zero ;
[ swap dup rot swap mod 0 = not ] 'not-factor ;
( tests )
100 factors .s .clr ( => 1 2 4 5 10 20 25 50 100 ) newline
53 factors .s .clr ( => 1 53 ) newline
64 factors .s .clr ( => 1 2 4 8 16 32 64 ) newline
12 factors .s .clr ( => 1 2 3 4 6 12 )
[edit] Objeck
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();
};
}
}
}
[edit] OCaml
let rec range = function 0 -> [] | n -> range(n-1) @ [n]
let factors n =
List.filter (fun v -> (n mod v) = 0) (range n)
[edit] Oz
declare
fun {Factors N}
Sqr = {Float.toInt {Sqrt {Int.toFloat N}}}
Fs = for X in 1..Sqr append:App do
if N mod X == 0 then
CoFactor = N div X
in
if CoFactor == X then %% avoid duplicate factor
{App [X]} %% when N is a square number
else
{App [X CoFactor]}
end
end
end
in
{Sort Fs Value.'<'}
end
in
{Show {Factors 53}}
[edit] Perl 6
Works with: Rakudo Star version 2010-08
sub factors (Int $n) {
sort +*, keys hash
map { $^x => 1, $n div $^x => 1 },
grep { $n %% $^x },
1 .. ceiling sqrt $n;
}
[edit] PHP
function GetFactors($n){
$factors = array(1, $n);
for($i = 2; $i * $i <= $n; $i++){
if($n % $i == 0){
$factors[] = $i;
if($i * $i != $n)
$factors[] = $n/$i;
}
}
sort($factors);
return $factors;
}
[edit] PL/I
do i = 1 to n;
if mod(n, i) = 0 then put skip list (i);
end;
[edit] PowerShell
[edit] Straightforward but slow
function Get-Factor ($a) {
1..$a | Where-Object { $a % $_ -eq 0 }
}
This one uses a range of integers up to the target number and just filters it using the Where-Object cmdlet. It's very slow though, so it is not very usable for larger numbers.
[edit] A little more clever
function Get-Factor ($a) {
1..[Math]::Sqrt($a) `
| Where-Object { $a % $_ -eq 0 } `
| ForEach-Object { $_; $a / $_ } `
| Sort-Object -Unique
}
Here the range of integers is only taken up to the square root of the number, the same filtering applies. Afterwards the corresponding larger factors are calculated and sent down the pipeline along with the small ones found earlier.
[edit] Perl
sub factors
{
my($n) = @_;
return grep { $n % $_ == 0 }(1 .. $n);
}
print join ' ',factors(64);
[edit] PicoLisp
(de factors (N)
(filter
'((D) (=0 (% N D)))
(range 1 N) ) )
[edit] PureBasic
Procedure PrintFactors(n)
Protected i, lim=Round(sqr(n),#PB_Round_Up)
NewList F.i()
For i=1 To lim
If n%i=0
AddElement(F()): F()=i
AddElement(F()): F()=n/i
EndIf
Next
;- Present the result
SortList(F(),#PB_Sort_Ascending)
ForEach F()
Print(str(F())+" ")
Next
EndProcedure
If OpenConsole()
Print("Enter integer to factorize: ")
PrintFactors(Val(Input()))
Print(#CRLF$+#CRLF$+"Press ENTER to quit."): Input()
EndIf
Output can look like
Enter integer to factorize: 96 1 2 3 4 6 8 12 16 24 32 48 96
[edit] Python
Naive and slow but simplest (check all numbers from 1 to n):
>>> def factors(n):
return [i for i in range(1, n + 1) if not n%i]
Slightly better (realize that there are no factors between n/2 and n):
>>> def factors(n):
return [i for i in range(1, n//2 + 1) if not n%i] + [n]
>>> factors(45)
[1, 3, 5, 9, 15, 45]
Much better (realize that factors come in pairs, the smaller of which is no bigger than sqrt(n)):
>>> from math import ceil, sqrt
>>> def factor(n):
return sorted(set(sum( ([x,n/x] for x in range(1, ceil(sqrt(n)) + 1) if not n%x), [] )))
>>> 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]
[edit] R
factors <- function(n)
{
if(length(n) > 1)
{
lapply(as.list(n), factors)
} else
{
one.to.n <- seq_len(n)
one.to.n[(n %% one.to.n) == 0]
}
}
factors(60)
1 2 3 4 5 6 10 12 15 20 30 60
factors(c(45, 53, 64))
[[1]]
[1] 1 3 5 9 15 45
[[2]]
[1] 1 53
[[3]]
[1] 1 2 4 8 16 32 64
[edit] Ruby
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 << i
f << self/i unless i == self/i
f
end.sort
end
end
[45, 53, 64].each {|n| p n.factors}
output
[1, 3, 5, 9, 15, 45] [1, 53] [1, 2, 4, 8, 16, 32, 64]
[edit] Sather
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;
[edit] Scala
def factor(n:Int) = (1 to Math.sqrt(n)).filter(n%_== 0).flatMap(x=>List(n/x,x)).toList.sort(_>_)
[edit] Scheme
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)
[edit] Slate
n@(Integer traits) primeFactors
[
[| :result |
result nextPut: 1.
n primesDo: [| :prime | result nextPut: prime]] writingAs: {}
].
where primesDo: is a part of the standard numerics library:
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."
].
[edit] Tcl
proc factors {n} {
set factors {}
for {set i 1} {$i <= sqrt($n)} {incr i} {
if {$n % $i == 0} {
lappend factors $i [expr {$n / $i}]
}
}
return [lsort -unique -integer $factors]
}
puts [factors 64]
puts [factors 45]
puts [factors 53]
output
1 2 4 8 16 32 64 1 3 5 9 15 45 1 53
[edit] Ursala
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>
