JavaScript - Factorial of a Number in JS

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.

Conclusion

JavaScript offers several ways to calculate factorials: iteration for simplicity, recursion for elegance, memoization for efficiency, and functional programming for concise code. The best method depends on your needs for performance and readability.

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