Function for prime factorisation of a number

PrimeFactorisation.hpp

/*
 * Header containing function primeFactorisation which returns std::map of prime factorisation of number
 * PROTOTYPE:
 * std::map<int, int> GS::primeFactorisation(int num);
 * 'num' is the number for which prime factorisation is required
 * In the map returned, for each element (i.e. pair), first element is factor and second is its power
 * E.g.
 * Prime factorisation of 49 = 2 * 7 * 7 = (2^1) * (7^2)
 * So, the map would contain pairs (2, 1) and (7, 2),
*/
#include <utility>
#include <map>

namespace GS
{

using std::map;
using std::make_pair;

map<int, int> primeFactorisation(int num)
{
	map<int, int>pf{};

	int fac, origNum = num;
	for (fac = 2; fac <= origNum/2 && num > 1; ++fac)
	{
		while (num % fac == 0)
		{
			num /= fac;
			auto ins = pf.insert(make_pair(fac, 1));
			if (!ins.second)
				++ins.first->second;
		}
	}
	
	return pf;
}

//namespace GS
}

/*
 * TEST CODE :
int main()
{
	int num;
	cin >> num;
	auto mp = GS::primeFactorisation(num);
	for (auto itr : mp)
	{
		if (itr != *mp.begin())
			cout << "* ";
		cout << "( " << itr.first << " ^ " << itr.second << " ) ";
	}
	
	return 0;
}
* 
* */