Python, count the trailing zeros within a factorial

Question

I am trying to calculate the number of trailing zeros in a factorial.

def count(x):
    zeros = 0                     
    for i in range (2,x+1): 
        print(i)
        if x > 0:
            if i % 5 == 0:       
                print("count")    
                zeros +=1       
        else:
            ("False")
    print(zeros)        

count(30)

I think the number of trailing zeros is incorrect.

When using count(30), there are 7 trailing 0‘s in 30. However it is returning 6.

Asked By: Oscar Dolloway

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Source

Answer 1

Your algorithm has problem:

import math

def count_zeroes(x):
    zeroes = 0
    if x <= 0:
        return zeroes
    for i in range(5, x+1, 5):
        for base in range(int(math.log(i, 5)), 0, -1):
            if i % pow(5, base) == 0:
                zeroes += base
                break
    return zeroes

Answered By: Philip Tzou

Answer 2

Wikipedia has a short article on this specific topic, which says that this can be computed with a straight-forward summation that counts factors of 5.

def trailing_zeros_of_factorial(n):
    assert n >= 0, n
    zeros = 0
    q = n

    while q:
        q //= 5
        zeros += q

    return zeros

# 32! = 263130836933693530167218012160000000
print(trailing_zeros_of_factorial(32)) # => 7

Answered By: user6732794

Answer 3

def count (x):
    i = 5
    zeros = 0
    while x >= i:
        zeros += x // i
        i *= 5
    return zeros

print(count(30))

Answered By: John Smith

Answer 4

We would first count the number of multiples of 5 between 1 and n (which is X ), then the number of multiples of 25 ( ~s ), then 125, and so on.
To count how many multiples of mare in n, we can just divide n by m

def countFactZeros(num):
    count = 0
    i = 5
    if num < 0:
        return False
    while num//i > 0:
        count = count + num//i
        i = i * 5
    return count

countFactZeros(10) # output should be 2
countFactZeros(100) # output should be 24

Answered By: Dheeraj Joshi

Answer 5

Try the following:

def zeros(n):
    x = n/5
    return x+zeros(x) if x else 0

Answered By: Artem Yambarshev

Python, count the trailing zeros within a factorial

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