What is Factorial of a number using JavaScript?

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Factorial of a number using JavaScript

JavaScript Program to Find Factorial of a Number using Recursion

The factorial of a non-negative integer is the product of all positive integers less than or equal to that number. It’s denoted by “n!” where n is the integer. Factorial represents the number of permutations or arrangements of a set.

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

JavaScript Program for Factorial

Examples:

Input : 4
Output : 24

Input : 5
Output : 120

Table of Content

Approach 1: Iterative Method
Approach 2: Recursive Method
Approach 3: Memoization Method

Approach 1: Iterative Method

Declare a variable with a value of the number whose factorial you have to find.
Declare a function factorial taking the value as a parameter.
In the function definition, initialize variable ans to 1.
Loop in the range of [2, n].
Multiply ans by the value of i in each iteration.
Return the value of ans.

Example: In this example, we a following iterative method.

Javascript

let n = 5; 

function factorial(n) { 
    let ans = 1; 
    
    if(n === 0)
        return 1;
    for (let i = 2; i <= n; i++) 
        ans = ans * i; 
    return ans; 
}

console.log(factorial(n));

Output

Time Complexity: O(n) Since the code is running for all the values of n

Space Complexity: O(1) As we are not allocating any extra space for a variable.

Approach 2: Recursive Method

Declare a variable with a value of the number whose factorial you have to find.
Declare a recursive function factorial taking the value as a parameter.
The function returns 1 if the value is 0 else the return calls the function for value – 1.
After recursion is over the value returned is the factorial.

Example: In this example, we are following Recursive method

Javascript

let n = 5;
function factorial(n) { 
    if (n === 0) { 
        return 1; 
    } 
    else { 
        return n * factorial( n - 1 ); 
    } 
} 

console.log(factorial(n));

Output

Time Complexity: O(n) Since the code is running for all the values of n

Space Complexity: O(n) As the stack is being created for each function call

Approach 3: Memoization Method

Declare a variable with the value of the number whose factorial you have to find.
Declare a function factorial taking the value and a cache (an array to store previously computed results) as parameters.
If the value is 0, return 1.
Check if the result for the current value is already stored in the cache. If it is, return the cached result.
If the result is not cached, calculate the factorial recursively and store the result in the cache.
Return the result from the cache.

Example: In this example, we follow the memoization method.

JavaScript

let n = 5;

function factorial(n, cache = []) {
    if (n === 0) {
        return 1;
    }
    if (cache[n] !== undefined) {
        return cache[n];
    }
    cache[n] = n * factorial(n - 1, cache);
    return cache[n];
}

console.log(factorial(n));