ProjectEuler#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 ?

#Algorithm from http://jonlandrum.com/2012/09/10/calculating-the-largest-prime-factor-of-a-number/
#1. Set the factor variable to 2 (the first prime)
#2. Determine if the user input is divisible by factor
#A. If so, repeatedly divide the user input by factor until it is not evenly divisible anymore. If the user input is #not divisible by factor, skip this step.
#B. Iterate factor to the next prime, and start step 2 again.
#3. Continue like so until the user input is equal to the final value of factor, which is then your answer.

def isPrime(n):
    '''check if integer n is a prime'''
    # range starts with 2 and only needs to go up the square-root of n
    for x in range(2, int(n**0.5)+1):
        if n % x == 0:
            return False
    return True

input = 600851475143
factor = 2

while input != factor:
    while input % factor == 0:
        input = input / factor

    factor += 1
    while not isPrime(factor):
        factor += 1


print input