Unlock the Power of Recursion: Calculating Factorials with Ease

The Factorial Formula: A Simple yet Powerful Concept

The factorial of a number is the product of all positive integers from 1 to that number. For instance, the factorial of 5 (denoted as 5!) is equal to:

1 × 2 × 3 × 4 × 5 = 120

This formula holds true for all positive integers, with one crucial exception: the factorial of 0 is defined as 1.

Tackling Negative Numbers: A Crucial Consideration

What about negative numbers, you ask? Well, the factorial of a negative number simply doesn’t exist. This is because the concept of factorial is inherently tied to the product of positive integers, which cannot be applied to negative numbers.

Implementing Recursion: A Step-by-Step Guide

So, how do we put this theory into practice? By leveraging JavaScript’s recursive capabilities, we can create a program that calculates factorials with ease. Here’s a sample program to get you started:

function factorial(num) {
  if (num < 0) {
    console.log("Error: Factorial is not defined for negative numbers.");
    return null;
  } else if (num === 0) {
    return 1;
  } else {
    return num * factorial(num - 1);
  }
}

const userInput = prompt("Enter a number:");
const num = parseInt(userInput);

if (isNaN(num)) {
  console.log("Error: Invalid input. Please enter a valid number.");
} else {
  const result = factorial(num);
  console.log(`The factorial of ${num} is ${result}.`);
}

The program works as follows:

• The user is prompted to enter a number.
• If the user enters a negative number, a message is displayed prompting them to enter a positive number.
• If the user enters a positive number or 0, the factorial(num) function is called.
• If the user enters 0, the program returns 1.
• If the user enters a number greater than 0, the program recursively calls itself by decreasing the number.
• This process continues until the number reaches 1, at which point 1 is returned.

By grasping the fundamental principles of recursion and applying them to factorial calculations, you’ll unlock a world of possibilities in mathematical computing.