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Python program to count number of trailing zeros in Factorial of number N

Learn how to count number of trailing zeros in factorial of N using Python program. By Ankit Rai Last updated : January 04, 2024

Problem statement

Given a number, write a Python program to count number of trailing zeros in factorial of N.

Formula used

Trailing 0s in N! = Count of 5s in prime factors of n!
    = floor(n/5) + floor(n/25) + floor(n/125) + ....

Example

Input: N = 23
Output: 4
Factorial of 23 is 25852016738884976640000 which has four trailing 0.

Input: N = 25
Output: 6
Factorial of 25 is 15511210043330985984000000 which has six trailing 0.

Python program to count number of trailing zeros in Factorial of number N

# Define a function for finding
# number of trailing zeros in N!
def find_trailing_zeros(num):
    sum = 0
    i = 1

    # iterating untill quotient is not zero
    while True:
        # take integer divison
        quotient = num // (5**i)
        if quotient == 0:
            break
        sum += quotient
        i += 1
    return sum


# Driver code
if __name__ == "__main__":
    # assigning a number
    num = 10

    # function call
    print(
        "Number of trailing zeros in factorial of",
        num,
        "is :",
        find_trailing_zeros(num),
    )
    num = 20
    print(
        "Number of trailing zeros in factorial of",
        num,
        "is :",
        find_trailing_zeros(num),
    )

Output

The output of the above example is:

Number of trailing zeros in factorial of 10 is : 2
Number of trailing zeros in factorial of 20 is : 4

Python Basic Programs »

To understand the above program, you should have the basic knowledge of the following Python topics:

• Python Variables
• Python Data Types
• Python print() Method
• Python Functions
• Python Loops