sorry, possibly too much info. was: Re: How can I speed up a script that iterates over a large range (600 billion)?

[John Salerno]

::sigh:: Well, I'm stuck again and it has to do with my get_factors
function again, I think. Even with the slight optimization, it's
taking forever on 20! (factorial, not excitement)  :) It's frustrating
because I have the Python right, but I'm getting stuck on the math.

The problem:

"What is the smallest positive number that is evenly divisible by all
of the numbers from 1 to 20?"



Here's the function (it's in the problem3.py file, hence the import
below):

import math

def get_factors(number):
    factors = []

    for n in range(2, int(math.sqrt(number))):
        if number % n == 0:
            factors.append(n)
            factors.append(number // n)

    return factors

And here's my new script for the new exercise:

import math
from problem3 import get_factors

max_num = 20
n = math.factorial(max_num)
factors = get_factors(n)
div_all = []

for x in factors:
    for y in range(2, max_num+1):
        if x % y != 0:
            break
        elif y == max_num:
            div_all.append(x)

print(min(div_all))

It could easily be that I'm simply approaching it all wrong. I just
thought that maybe using the factorial of the highest number in the
range (in this case, 20) would be an easy way of finding which numbers
to test.