biggestfactor.py

import math

def isprime(n):
    if n == 2:
        return True
    if n == 3:
        return True
    if n % 2 == 0:
        return False
    if n % 3 == 0:
        return False
    i = 5
    w = 2
    while i * i <= n:
        if n % i == 0:
            return False
        i += w
        w = 6 - w
    return True

num = 600851475143
#num = 6858
r = num
factors = []
root = (num/2)+1
i=2
while i < root+1:
    if isprime((i)):
        if r > 1:
            while (r/i)*i == r:
                r = (r/i)
                factors.append(i)
        else:
            break
    i += 1

if len(factors) == 0:
    print("Number %d is prime" % num)
else:
    print("Largest prime factor = %d" % factors[-1])

print(factors)