Python: Find the number of zeros at the end of a factorial of a given positive number

Last update on April 17 2025 13:01:42 (UTC/GMT +8 hours)

Factorial Trailing Zeros

Write a Python program to find the number of zeros at the end of a factorial of a given positive number.

Range of the number(n): (1 ≤ n ≤ 2*109).

Sample Solution:

Python Code:

# Define a function 'factendzero' that calculates the number of trailing zeros
# in the factorial of a given number 'n'.
def factendzero(n):
    # Initialize variables 'x' and 'y'.
    x = n // 5
    y = x 
    
    # Use a while loop to iteratively calculate the number of trailing zeros.
    while x > 0:
        x /= 5
        y += int(x)
    
    return y  # Return the final count of trailing zeros.

# Test the 'factendzero' function with different values of 'n' and print the results.
print(factendzero(5))
print(factendzero(12))
print(factendzero(100))

Sample Output:

1
2
24

Explanation:

The above Python code defines a function "factendzero()" that calculates the number of trailing zeros in the factorial of a given number 'n'. Here's a brief explanation:

• Function Definition:
• def factendzero(n):: Define a function named "factendzero" that takes an integer 'n' as input.
• Variable Initialization:
• x = n // 5: Initialize a variable 'x' to the integer division of 'n' by 5.
• y = x: Initialize another variable 'y' with the same value as 'x'.
• While Loop:
• while x > 0:: Enter a while loop that continues as long as 'x' is greater than 0.
• x /= 5: Divide 'x' by 5 in each iteration.
• y += int(x): Add the integer value of 'x' to 'y'.
• Return Result:
• return y: Return the final count of trailing zeros.
• Function Testing:
• print(factendzero(5)): Test the function with the input 5 and print the result.
• print(factendzero(12)): Test the function with the input 12 and print the result.
• print(factendzero(100)): Test the function with the input 100 and print the result.

Visual Presentation:

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to calculate the number of digits in the factorial of a given number.
• Write a Python program to determine the number of leading zeros in the factorial of a number in a specified base.
• Write a Python program to compute the prime factorization of a factorial number.
• Write a Python program to find the sum of the digits in the factorial of a given number.

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