Writing Factorial Recursively

When it comes to solving mathematical problems in programming, the factorial is a commonly encountered concept. In this tutorial, we will explore how to write a factorial function recursively using JavaScript.

What is a factorial?

A factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n. It can be defined recursively as follows:

• 0! = 1 (base case)
• n! = n * (n-1)! for n > 0 (recursive case)

Step-by-step Implementation

To write a factorial function recursively in JavaScript, follow these steps:

Step 1: Identify the Base Case

The base case for the factorial function is when n is equal to 0. In this case, the factorial is 1.

function factorial(n) {
  if (n === 0) {
    return 1;
  }
}

Step 2: Implement the Recursive Case

In the recursive case, we multiply n with the factorial of n-1. We can call the factorial function itself to calculate the factorial of n-1.

function factorial(n) {
  if (n === 0) {
    return 1;
  }

  return n * factorial(n - 1);
}

Step 3: Test the Function

Let’s test our factorial function with a few example inputs:

console.log(factorial(0)); // Output: 1
console.log(factorial(5)); // Output: 120
console.log(factorial(10)); // Output: 3628800

Summary

In this tutorial, we learned how to write a factorial function recursively in JavaScript. By breaking the problem down into smaller subproblems and leveraging the concept of recursion, we were able to create an elegant and concise solution to calculate factorials.

Remember, recursion is a powerful technique in programming, but it is essential to identify the base case and define the recursive case properly to avoid infinite loops. With practice, you can become proficient in writing recursive functions and solve a wide range of problems efficiently.

Happy coding!