Solution for Project Euler's problem number 3 in Python

Problem 3 - Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ?

Simplest solution

its time complexity is O(n) (linear) with the largest factor

It means it's fast for 600851475143 but not for 600851475145

def get_prime_factors(number):
    factor=2
    while number <> 1 & factor <= number:
        factor += 1
        while number % factor == 0:
            yield factor
            number /= factor

for x in get_prime_factors(600851475143):
    print x

Fastest solution

its time complexity is O(sqrt(n)) (fractional power) with the largest factor.

def get_prime_factors(number):
    while number % 2 == 0:
        yield 2
        number /= 2
    factor=1
    maxFactor = int(number ** .5)
    while number <> 1 & factor <= maxFactor:
        factor += 2
        while number % factor == 0:
            yield factor
            number /= factor
    if number > 1:
        yield number    

for x in get_prime_factors(600851475145):
    print x