Write A Recursive Function for Calculating N Factorial: N

What is Factorial?

The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. The factorial of 0 is defined as 1.

For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Factorials are used in permutations, combinations, probability calculations, and many other mathematical and computational applications.

Writing the Recursive Function

A recursive function is one that calls itself in order to solve a problem. To calculate n factorial recursively, we can use the following approach:

1. Base case: If n is 0 or 1, return 1.
2. Recursive case: Return n multiplied by the factorial of n-1.

Here's the JavaScript implementation:

function factorial(n) {
    if (n === 0 || n === 1) {
        return 1;
    } else {
        return n * factorial(n - 1);
    }
}

Example Calculation

Let's calculate 4! using our recursive function:

1. factorial(4) calls factorial(3)
2. factorial(3) calls factorial(2)
3. factorial(2) calls factorial(1)
4. factorial(1) returns 1 (base case)
5. factorial(2) returns 2 × 1 = 2
6. factorial(3) returns 3 × 2 = 6
7. factorial(4) returns 4 × 6 = 24

So, 4! = 24.