The factorial of a number is a mathematic concept used in many areas like counting possibilities and solving problems. The factorial of a number n, written as n!, is the result of multiplying all the whole numbers from 1 up to n.

Logic

n!=n×(n−1)×(n−2)×⋯×1

Note: Factorials of negative numbers are not defined as only positive numbers including 0 are defined in the domain of factorials.

1. Using Iteration

This method uses a simple loop to calculate the factorial. It is simple and easy to understand.

function fact(n) {
    let res = 1;
    for (let i = 1; i <= n; i++) {
        res *= i;
    }
    return res;
}
console.log(fact(5));

Output

120

We use a loop to multiply numbers from 1 to n. The result variable accumulates the product.

2. Using Recursion

The recursion involves a function that calls itself until it reaches a base condition. It is elegant but can be less efficient for large numbers.

function fact(n) {
    if (n === 0 || n === 1) {
        return 1;
    }
    return n * fact(n - 1);
}
console.log(fact(5));

Output

120

The function calls itself with a decremented value of until it reaches the base case and then at last returns the final value from it.

3. Using a While Loop

This method uses a while loop to repeatedly multiply numbers. It is similar to iteration but offers a different looping structure.

function fact(n) {
    let res = 1;
    while (n > 1) {
        res *= n;
        n--;
    }
    return res;
}
console.log(fact(5));

Output

120

The while loop repeatedly multiplies result by n and decrements n until it reaches 1.

4. Using Memoization

Memoization stores previously calculated results, improving efficiency for repeated calls. It uses a closure for caching.

const fact = (function () {
    const cache = {};
    return function facto(n) {
        if (n === 0 || n === 1) {
            return 1;
        }
        if (cache[n]) {
            console.log("value from caeche")
            return cache[n];
        }
        cache[n] = n * facto(n - 1);
        return cache[n];
    };
})();
console.log(fact(5))

Output

120

• This code defines a self-invoking function that returns a facto function, which calculates the factorial of a number while using caching for efficiency.
• The cache object stores previously calculated results to avoid redundant computations.
• If the input number is already in the cache, it retrieves the value; otherwise, it calculates the factorial recursively.

5. Using Functional Programming

This approach uses array methods and functional programming paradigms. It is concise and elegant.

const fact = (n) =>
    n === 0 || n === 1
        ? 1
        : Array.from({ length: n }, (_, i) => i + 1).reduce(
            (acc, num) => acc * num,
            1
        );
console.log(fact(5));

Output

120

• This code defines a function fact using an arrow function to calculate the factorial of a number.
• It uses a ternary operator to return 1 for inputs 0 or 1.
• For other numbers, it creates an array of numbers from 1 to n and uses the reduce method to compute the product.

JavaScript Program to Find the Factorial of a Number

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JavaScript Program to Find the Factorial of a Number

Factorial of a number using JavaScript