# Largest prime factor

Largest prime factor is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Task

The task description is taken for Project Euler (https://projecteuler.net/problem=3)
What is the largest prime factor of the number 600851475143 ?

## BASIC

### FreeBASIC

<lang freebasic>#include"isprime.bas" dim as ulongint n = 600851475143, j = 3 while not isprime(n)

```   if n mod j = 0 then n/=j
j+=2
```

wend print n</lang>

Output:
`6857`

### GW-BASIC

No primality testing is even required. <lang gwbasic>10 N#=600851475143# 20 J#=3 30 IF J#=N# THEN GOTO 100 40 IF INT(N#/J#) = N#/J# THEN N# = N#/J# 50 J#=J#+2 60 GOTO 30 100 PRINT N#</lang>

Output:
`6857`

## C

<lang c>#include <stdio.h>

1. include <stdlib.h>

int isprime( long int n ) {

```   int i=3;
if(!(n%2)) return 0;
while( i*i < n ) {
if(!(n%i)) return 0;
i+=2;
}
return 1;
```

}

int main(void) {

```   long int n=600851475143, j=3;
```
```   while(!isprime(n)) {
if(!(n%j)) n/=j;
j+=2;
}
printf( "%ld\n", n );
return 0;
```

}</lang>

Output:
`6857`

## Fermat

<lang fermat>n:=600851475143; j:=3; while Isprime(n)<>1 do

```   if Divides(j, n) then n:=n/j fi;
j:=j+2;
```

od; !!n;</lang>

Output:
`6857`

## Go

Translation of: Wren

<lang go>package main

import "fmt"

func largestPrimeFactor(n uint64) uint64 {

```   if n < 2 {
return 1
}
inc := [8]uint64{4, 2, 4, 2, 4, 6, 2, 6}
max := uint64(1)
for n%2 == 0 {
max = 2
n /= 2
}
for n%3 == 0 {
max = 3
n /= 3
}
for n%5 == 0 {
max = 5
n /= 5
}
k := uint64(7)
i := 0
for k*k <= n {
if n%k == 0 {
max = k
n /= k
} else {
k += inc[i]
i = (i + 1) % 8
}
}
if n > 1 {
return n
}
return max
```

}

func main() {

```   n := uint64(600851475143)
fmt.Println("The largest prime factor of", n, "is", largestPrimeFactor(n), "\b.")
```

}</lang>

Output:
```The largest prime factor of 600851475143 is 6857.
```

## Julia

<lang julia> using Primes

@show first(last(factor(600851475143).pe))

</lang>
Output:
`first(last((factor(600851475143)).pe)) = 6857`

## PARI/GP

<lang parigp>A=factor(600851475143) print(A[matsize(A)[1],1])</lang>

Output:
`6857`

## Raku

Pure Raku, not particularly fast. <lang perl6>use Prime::Factor;

my \$start = now;

for flat 600851475143, (1..∞).map: { 2 +< \$_ - 1 } {

```   say "Largest prime factor of \$_: ", .&prime-factors.max;
exit if now - \$start > 1.0; # quit after one second of run time
```

}</lang>

```Largest prime factor of 600851475143: 6857
Largest prime factor of 3: 3
Largest prime factor of 7: 7
Largest prime factor of 15: 5
Largest prime factor of 31: 31
Largest prime factor of 63: 7
Largest prime factor of 127: 127
Largest prime factor of 255: 17
Largest prime factor of 511: 73
Largest prime factor of 1023: 31
Largest prime factor of 2047: 89
Largest prime factor of 4095: 13
Largest prime factor of 8191: 8191
Largest prime factor of 16383: 127
Largest prime factor of 32767: 151
Largest prime factor of 65535: 257
Largest prime factor of 131071: 131071
Largest prime factor of 262143: 73
Largest prime factor of 524287: 524287
Largest prime factor of 1048575: 41
Largest prime factor of 2097151: 337
Largest prime factor of 4194303: 683
Largest prime factor of 8388607: 178481
Largest prime factor of 16777215: 241
Largest prime factor of 33554431: 1801
Largest prime factor of 67108863: 8191
Largest prime factor of 134217727: 262657
Largest prime factor of 268435455: 127
Largest prime factor of 536870911: 2089
Largest prime factor of 1073741823: 331
Largest prime factor of 2147483647: 2147483647
Largest prime factor of 4294967295: 65537
Largest prime factor of 8589934591: 599479
Largest prime factor of 17179869183: 131071
Largest prime factor of 34359738367: 122921
Largest prime factor of 68719476735: 109
Largest prime factor of 137438953471: 616318177
Largest prime factor of 274877906943: 524287
Largest prime factor of 549755813887: 121369
Largest prime factor of 1099511627775: 61681
Largest prime factor of 2199023255551: 164511353
Largest prime factor of 4398046511103: 5419
Largest prime factor of 8796093022207: 2099863
Largest prime factor of 17592186044415: 2113
Largest prime factor of 35184372088831: 23311
Largest prime factor of 70368744177663: 2796203
Largest prime factor of 140737488355327: 13264529
Largest prime factor of 281474976710655: 673
Largest prime factor of 562949953421311: 4432676798593
Largest prime factor of 1125899906842623: 4051
Largest prime factor of 2251799813685247: 131071
Largest prime factor of 4503599627370495: 8191
Largest prime factor of 9007199254740991: 20394401
Largest prime factor of 18014398509481983: 262657
Largest prime factor of 36028797018963967: 201961
Largest prime factor of 72057594037927935: 15790321
Largest prime factor of 144115188075855871: 1212847
Largest prime factor of 288230376151711743: 3033169
Largest prime factor of 576460752303423487: 3203431780337
Largest prime factor of 1152921504606846975: 1321
Largest prime factor of 2305843009213693951: 2305843009213693951
Largest prime factor of 4611686018427387903: 2147483647
Largest prime factor of 9223372036854775807: 649657
Largest prime factor of 18446744073709551615: 6700417
Largest prime factor of 36893488147419103231: 145295143558111
Largest prime factor of 73786976294838206463: 599479
Largest prime factor of 147573952589676412927: 761838257287
Largest prime factor of 295147905179352825855: 131071
Largest prime factor of 590295810358705651711: 10052678938039
Largest prime factor of 1180591620717411303423: 122921
Largest prime factor of 2361183241434822606847: 212885833
Largest prime factor of 4722366482869645213695: 38737
Largest prime factor of 9444732965739290427391: 9361973132609
Largest prime factor of 18889465931478580854783: 616318177
Largest prime factor of 37778931862957161709567: 10567201
Largest prime factor of 75557863725914323419135: 525313
Largest prime factor of 151115727451828646838271: 581283643249112959
Largest prime factor of 302231454903657293676543: 22366891
Largest prime factor of 604462909807314587353087: 1113491139767
Largest prime factor of 1208925819614629174706175: 4278255361
Largest prime factor of 2417851639229258349412351: 97685839
Largest prime factor of 4835703278458516698824703: 8831418697
Largest prime factor of 9671406556917033397649407: 57912614113275649087721
Largest prime factor of 19342813113834066795298815: 14449
Largest prime factor of 38685626227668133590597631: 9520972806333758431
Largest prime factor of 77371252455336267181195263: 2932031007403
Largest prime factor of 154742504910672534362390527: 9857737155463
Largest prime factor of 309485009821345068724781055: 2931542417
Largest prime factor of 618970019642690137449562111: 618970019642690137449562111
Largest prime factor of 1237940039285380274899124223: 18837001
Largest prime factor of 2475880078570760549798248447: 23140471537
Largest prime factor of 4951760157141521099596496895: 2796203
Largest prime factor of 9903520314283042199192993791: 658812288653553079```

## Ring

<lang ring> load "stdlib.ring" see "working..." + nl see "The largest prime factor of the number 600851475143 is:" + nl num = 600851475143 numSqrt = sqrt(num) numSqrt = floor(numSqrt) if numSqrt%2 = 0

```  numSqrt++
```

ok

for n = numSqrt to 3 step -2

```   if isprime(n) and num%n = 0
exit
ok
```

next

see "" + n + nl see "done..." + nl </lang>

Output:
```working...
The largest prime factor of the number 600851475143 is:
6857
done...
```

## Wren

Without using any library functions at all (it's a one-liner otherwise): <lang ecmascript>var largestPrimeFactor = Fn.new { |n|

```   if (!n.isInteger || n < 2) return 1
var inc = [4, 2, 4, 2, 4, 6, 2, 6]
var max = 1
while (n%2 == 0) {
max = 2
n = (n/2).floor
}
while (n%3 == 0) {
max = 3
n = (n/3).floor
}
while (n%5 == 0) {
max = 5
n = (n/5).floor
}
var k = 7
var i = 0
while (k * k <= n) {
if (n%k == 0) {
max = k
n = (n/k).floor
} else {
k = k + inc[i]
i = (i + 1) % 8
}
}
return (n > 1) ? n : max
```

}

var n = 600851475143 System.print("The largest prime factor of %(n) is %(largestPrimeFactor.call(n)).")</lang>

Output:
```The largest prime factor of 600851475143 is 6857.
```