Introduction to JavaScript

JavaScript Program to Find Prime Factors

Last Updated : 04 Jun, 2024

In this article, we will see all the methods to find the prime factors of a number using JavaScript.

Methods to Find Prime Factors:

Table of Content

Method 1: Using loops and Math.pow() Method

In this method, we will use a JavaScript loop to iterate the possible factors and Math.pow() method to get the square root of the number. Instead of Math.pow() method, we can also use Math.sqrt() or i*i < n condition.

Example:

JavaScript

function isPrime(i) {
    if (i == 2) return true;
    for (let j = 2; j < Math.pow(i, 0.5) + 1; ++j) {
        if (i % j === 0) return false;
    }
    return true;
}
function prime(n) {
    let result = [];
    for (let i = 2; i < Math.pow(n, 0.5); i++) {
        if (n % i == 0 && isPrime(i)) result.push(i);
        if (n % i == 0 && isPrime(n/i)) result.push(n/i);

    }
    return result.sort((a,b)=>a-b);
}

const num = 85;
console.log("Prime factors of " + 
    num + ": " + prime(num));

Output

Prime factors of 85: 5,17

Method 2: Recursive Approach with Spread Operator

In this method, we will call the function recursively and return the output with the spread operator to get the array output.

Example:

JavaScript

function recursivePrime(n, d) {
    if (n <= 1) return [];
    if (n == 2) return [2];
    flag = false;
    while (n % d == 0) {
        n /= d;
        flag = true;
    }
    if (flag) return [d, ...recursivePrime(n, d + 1)];
    return recursivePrime(n, d + 1);
}

const num = 85;
console.log(
    "Prime factors of " +
        num + ": " +
        recursivePrime(num, 2)
);

Output

Prime factors of 85: 5,17

Method 3: Sieve of Eratosthenes Algorithm

The Sieve of Eratosthenes is an efficient algorithm for finding all prime numbers up to a specified integer. We can modify this algorithm slightly to find the prime factors of a given number.

Example:

JavaScript

function primeFactorsSieve(n) {
    const primes = [];
    const smallestPrimeFactor = new Array(n + 1).fill(0);
    
    for (let i = 2; i <= n; ++i) {
        if (smallestPrimeFactor[i] === 0) {
            smallestPrimeFactor[i] = i;
            primes.push(i);
        }
        
        for (let j = 0; j < primes.length && primes[j] <= smallestPrimeFactor[i] && i * primes[j] <= n; ++j) {
            smallestPrimeFactor[i * primes[j]] = primes[j];
        }
    }
    
    const factors = [];
    while (n > 1) {
        factors.push(smallestPrimeFactor[n]);
        n /= smallestPrimeFactor[n];
    }
    
    return factors;
}

const num = 85;
console.log("Prime factors of " + num + ": " + primeFactorsSieve(num));

Output

Prime factors of 85: 5,17

Prime Factors Using JavaScript

Introduction to JavaScript

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