Factorial Trailing Zeroes Calculator

# This code find the number of trailing zeroes in a factorial.
# The number of zeroes is the lesser of "factors of two" and "factors of five" in all the numbers of the factorial expansion.
# (Since there are more twos than fives, and every two, times five, equals a 10, which leads to one trailing zero, it depends only on factors of five.)

import math
import random

twos = 0
fives = 0
remainders_two = []
remainders = []
factorial = 1000000

#

for i in range(60):
    factorial = random.randint(10,10000000)
    print("Factorial of", factorial, "has about", factorial/4, "zeroes.")
    factemp=factorial
    while True:
        twos += factemp // 2
        remainders_two.append(math.floor(factemp % 2))
        factemp = factemp / 2
        if factemp < 1:
            break

#    factorial = (10**i)*10
    factemp=factorial
    while True:
        fives += factemp // 5
        remainders.append(math.floor(factemp % 5))
        factemp = factemp / 5
        if factemp < 1:
            break

#    factorial = (10**i)*1000000

#    print("For the numbers 1-10^"+str(math.log10(factorial)))
#    print(factorial-twos, "factors of two less than expected 1")
    print("Calculated zeroes:", fives)
    print("Remainders:", remainders)
    print("Sum of remainders, divided by 4:", sum(remainders)/4)
    print("--")
    print("Calculated twos:", twos)
    print("Remainders:", remainders_two)
    print("Sum of remainders, divided by 1:", sum(remainders_two))
    if sum(remainders)/4 == factorial/4-fives and sum(remainders_two) == factorial-twos:
        print("MATCH!")
    else:
        print("DOES NOT MATCH!")
        break
    print()
    twos = 0
    fives = 0
    remainders_two.clear()
    remainders.clear()