Python Program to Calculate the Factorial Using Recursion

Introduction

Factorial is a mathematical operation that multiplies a given number by every positive integer less than it. The factorial of a number n is denoted as n! and is calculated as:

• n! = n * (n-1) * (n-2) * ... * 1
• 0! = 1 (by definition)

Recursion is an effective method to calculate the factorial of a number, as it allows you to express the factorial in terms of smaller factorials. This tutorial will guide you through creating a Python program that calculates the factorial of a number using recursion.

Example:

• Function Name: factorial
• Function Purpose: Calculate the factorial of a given number using recursion.
• Program Output:

  Factorial of 5 is 120
  

Problem Statement

Create a Python program that:

• Defines a recursive function named factorial.
• The function takes a single argument, n.
• The function calculates the factorial of n using recursion.
• The program calls the function with a sample value to demonstrate its usage.

Solution Steps

1. Define the Recursive Function: Use the def keyword to define a function named factorial.
2. Add a Base Case: Include a base case to stop the recursion when n equals 1 or 0.
3. Implement the Recursive Case: In the recursive case, call the factorial function itself with n-1.
4. Call the Function: Call the factorial function with a sample value, such as 5.
5. Display the Result: Print the result returned by the function.

Python Program

# Python Program to Calculate the Factorial Using Recursion
# Author: https://www.rameshfadatare.com/

# Step 1: Define the recursive function
def factorial(n):
    # Step 2: Add a base case
    if n == 0 or n == 1:
        return 1
    # Step 3: Implement the recursive case
    else:
        return n * factorial(n - 1)

# Step 4: Call the function with a sample value
result = factorial(5)

# Step 5: Display the result
print(f"Factorial of 5 is {result}")

Explanation

Step 1: Define the Recursive Function

• The function factorial is defined using the def keyword. It takes one parameter, n, which is the number for which the factorial is calculated.

Step 2: Add a Base Case

• The base case checks if n is 0 or 1. If so, the function returns 1 because the factorial of 0 and 1 is 1. The base case is essential to stop the recursion and prevent an infinite loop.

Step 3: Implement the Recursive Case

• If n is not 0 or 1, the function calls itself with n-1. This reduces the problem size and recursively calculates the factorial until the base case is reached.

Step 4: Call the Function

• The factorial function is called with the value 5. This initiates the recursion process.

Step 5: Display the Result

• The result of the function is stored in the result variable, and the print() function is used to display the factorial of 5.

Output Example

Example Output:

Factorial of 5 is 120

Additional Examples

Example 1: Factorial of 0

# Calling the function to calculate the factorial of 0
result = factorial(0)
print(f"Factorial of 0 is {result}")

Output:

Factorial of 0 is 1

Example 2: Factorial of 7

# Calling the function to calculate the factorial of 7
result = factorial(7)
print(f"Factorial of 7 is {result}")

Output:

Factorial of 7 is 5040

Example 3: Factorial of 1

# Calling the function to calculate the factorial of 1
result = factorial(1)
print(f"Factorial of 1 is {result}")

Output:

Factorial of 1 is 1

Conclusion

This Python program demonstrates how to calculate the factorial of a number using recursion. Recursion is a powerful technique that allows you to solve problems by breaking them down into smaller instances of the same problem. Understanding how to implement recursive functions is essential for solving a wide range of problems in Python and other programming languages.