Eulers problem №3, code stucks on big numbers

Question

I'm currently learning Python, and practice with euler's problem's. I'm stuck on 3rd problem, my code didn't working on the big numbers, but with other number's it's working.

n = 600851475143 
x = 0
for i in range(2,n):
    if(n%i == 0):
        if(x < i): x = i
print(x)

The console just didn't get any results and stucks. P.S https://projecteuler.net/problem=3

(sorry for my bad english)

Answer 1

It's running, but just the time it takes is huge. You can check by the following code, it keeps going to print x's.

n = 600851475143
x = 0
for i in range(2, n):
    if n % i == 0:
        if x < i:
            x = i
            print(x)

---

To save time, you can try the following code instead of your code:

n = 600851475143
x = 0
for i in range(2, n):
    if n % i == 0:
        x = n // i
        break
print(x) 

which prints 8462696833 instantly. But as @seesharper stated on the comment, it is merely the largest factor and not a prime factor. So it is not the correct answer to the Project Euler Problem #3.

Answer 2

Check this code you will save a lot of time

Using sqrt for optimization

from math import sqrt
def Euler3(n):
    x=int(sqrt(n))
    for i in range(2,x+1):
        while n % i == 0:
            n //= i
            if n == 1 or n == i:
                return i
    return n
n = int(input())
print(Euler3(n))

---

Also, check my Euler git repo

There are only 6 solutions in python2 and it's pretty old but they are very well optimized.