Factorial Calculation in Python

This document explains how to calculate the factorial of a given number using a Python program. The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is denoted as n! and is defined as:

        n! = n * (n-1) * (n-2) * ... * 1

Python Program

The following Python program calculates the factorial of a given number using a recursive function:

def factorial(n):
    """
    Calculate the factorial of a given number n.

    Args:
        n (int): The number to calculate the factorial for.

    Returns:
        int: The factorial of the number n.

    Raises:
        ValueError: If n is a negative integer.
    """
    if n < 0:
        raise ValueError("Factorial is not defined for negative numbers.")
    if n == 0 or n == 1:
        return 1
    else:
        return n * factorial(n - 1)

# Example usage
if __name__ == "__main__":
    try:
        number = int(input("Enter a number to calculate its factorial: "))
        result = factorial(number)
        print(f"The factorial of {number} is {result}.")
    except ValueError as e:
        print(e)

Explanation

The factorial function is defined to calculate the factorial of a non-negative integer n. The function follows these steps:

• If n is less than 0, it raises a ValueError because the factorial is not defined for negative numbers.
• If n is 0 or 1, the function returns 1 because 0! = 1 and 1! = 1 by definition.
• For other values of n, the function recursively calls itself with n-1 and multiplies the result by n.

The example usage section prompts the user to enter a number and then calculates and prints its factorial.

How to Run the Program

To run the program, copy the Python code into a file named factorial.py and execute it using a Python interpreter. For example:

python factorial.py

When prompted, enter a non-negative integer to see the factorial calculation result.