Find the largest prime factor of a composite number

improved.js

var x = 600851475143,
    getLargestPrimeFactor = function(n) {
        var largestPrimeFactor,
            factor = 2;

        while (n > 1) {
            if (n % factor === 0) {
                largestPrimeFactor = factor;
                n = n / factor;
                while (n % factor === 0) {
                    n = n / factor;
                }
            }

            factor += (factor === 2) ? 1 : 2;
        }

        return largestPrimeFactor;
    };

console.log(getLargestPrimeFactor(x));

original.js

var x = 600851475143,
    isPrime = function(n) {
        if (n === 2) return true;
        if (n % 2 === 0) return false;
        for (var factor = 3; factor <= Math.sqrt(n); factor += 2)
            if (n % factor === 0) return false;

        return true;
    },
    getLargestPrimeFactor = function(n) {
        var largestPrimeFactor;

        for (var factor = 2; factor <= Math.sqrt(n); factor++)
            if (n % factor === 0 && isPrime(factor))
                largestPrimeFactor = factor;

        return largestPrimeFactor;
    };

console.log(getLargestPrimeFactor(x));

You could use an array instead and use array.push(largestPrimeFactor); after line 8. This would create an array with the prime factors.