C program to find factorial of a number using recursion

The factorial of a number is a fundamental concept in mathematics, often denoted by n!, where n is a non-negative integer. It is defined as the product of all positive integers up to n. Factorials have widespread applications in permutations, combinations, and various fields of mathematics and computer science. In this article, we will focus on writing a C program to find the factorial of a number using recursion. We will explain the concept of recursion, outline the algorithm, and provide a complete C program with detailed explanations.

Understanding Factorials

The factorial of a non-negative integer n is calculated as:

n! = n x (n-1) x (n-2) x … x 2 x 1

The factorial of 0 is defined as 1, i.e., 0! = 1.

Concept of Recursion

Recursion is a programming technique where a function calls itself to solve smaller instances of the same problem. It consists of two main parts:

1. Base Case: The condition under which the recursive function stops calling itself.
2. Recursive Case: The part where the function calls itself with modified parameters.

Algorithm to Find Factorial Using Recursion

To calculate the factorial of a number using recursion, follow these steps:

1. Base Case: If n is 0 or 1, return 1 as the factorial of 0 or 1 is 1.
2. Recursive Case: For n > 1, return n * factorial(n - 1).

Write a C program to find factorial of a number using recursion

Below is the C program to find the factorial of a number using recursion:

#include <stdio.h>

// Recursive function to find factorial of a number
int factorial(int n) {
    // Base case: Factorial of 0 or 1 is 1
    if (n == 0 || n == 1)
        return 1;
    // Recursive case: n * factorial of (n-1)
    else
        return n * factorial(n - 1);
}

int main() {
    int number;

    // Input the number from the user
    printf("Enter a number to find its factorial: ");
    scanf("%d", &number);

    // Check for negative numbers
    if (number < 0) {
        printf("Factorial of a negative number is not defined.");
    } else {
        // Calculate factorial using recursive function
        int result = factorial(number);
        // Output the result
        printf("Factorial of %d is %d.", number, result);
    }

    return 0;
}

Output

Enter a number to find its factorial: 7
Factorial of 7 is 5040.

Explanation of the Code

1. Recursive Function factorial:
   • This function takes an integer n as an argument and returns the factorial of n.
   • Base Case: If n is 0 or 1, the function returns 1.
   • Recursive Case: For n > 1, the function returns n * factorial(n - 1), which recursively calls itself with the argument n - 1.
2. Main Function main:
   • The user is prompted to enter a number.
   • The function checks if the number is negative, as factorial is not defined for negative numbers.
   • The factorial function is called with the user-provided number, and the result is stored in the variable result.
   • The factorial result is then printed.

Example Runs

Example 1

Enter a number to find its factorial: 5
Factorial of 5 is 120.

Example 2

Enter a number to find its factorial: 0
Factorial of 0 is 1.

Example 3

Enter a number to find its factorial: -3
Factorial of a negative number is not defined.