The way I factorize an integer into prime factors ...

factorize.cpp

// factorize() - factorize an integer into prime factors
std::vector<int> factorize(int n) {
	std::vector<int> factors;
	int maxFactor = std::sqrt(n);

	for (int factor = 2; factor <= maxFactor; factor++) {
		while (n % factor == 0) {
			factors.push_back(factor);
			n /= factor;
		}
		if (n == 1)
			return factors;
	}

	factors.push_back(n);
	return factors;
}