Project Euler - Problem 3 - Largest prime factor

What is the largest prime factor of the given number?

The problem

This is problem 3 from the Project Euler.

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the given number?

First of all, what is a prime number?

According to Wikipedia:

prime numbers are the natural numbers greater than one that are not products of two smaller natural numbers.

And from Fact Monster:

A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1.

Let’s begin

Initialise variables and common functions:

// list of numbers we wanna test
var test_values = [2, 3, 5, 7, 13195, 600851475143];

// this function execute the code and records the time to execute
function run_function(func, test_values) {
  for(var i in test_values){
    console.log('Test value:', test_values[i]);
    var t0 =;
    console.log('Output:', func(test_values[i]));
    var t1 =;
    console.log("Took " + (t1 - t0) + " ms");

Attempt #1: for-loop, divide number check reminder

Since all even numbers can be divided by 2, we shall return 2 for every even input number. That’s the easy part.

When the input number is an odd number, we need to do some division to check for whole numbers.

A prime number cannot be formed by multiplying two smaller whole numbers, so we divide the odd numbers i to check if the division produces any reminder (decimal values).

If dividing odd number i result in a value with a reminder, i is not a prime number to the input number.

If dividing odd number i is a whole number, then i is one of the prime numbers for input number.

function largestPrimeFactor(number) {

  // only even prime number is 2. All other even numbers can be divided by 2.
    return 2;

  // test the odd numbers, greater than 3
  var list_of_prime_numbers = [];
  var i = 3;

  // check the division of the input number and i variable
  // if division no reminder, it is one of the prime numbers
  // if not, increase i by 2 to test the next odd number
  while(number != 1){
    if(number % i === 0){
      number /= i;
      i+=2; // increase by 2 to test the next odd number

  // return the last prime value
  return list_of_prime_numbers[list_of_prime_numbers.length-1];

run_function(largestPrimeFactor, test_values);

The output:

Test value: 2
Output: 2
Took 0.0949999998738349 ms

Test value: 3
Output: 3
Took 0.019999999949504854 ms

Test value: 5
Output: 5
Took 0.06500000017695129 ms

Test value: 7
Output: 7
Took 0.030000000151630957 ms

Test value: 13195
Output: 29
Took 0.02500000027794158 ms

Test value: 600851475143
Output: 6857
Took 0.2799999997478153 ms

Here’s my solution, can it be any better?

This is my Project Euler Challenge journey; anyone wants to do this together? It will be fun and we can learn a thing or two by solving this problem in different ways.

Full Code

Thanks for reading!