Factorial of large numbers

factorial.cpp

#include <iostream>
#include <algorithm>
#include <string>
#include <chrono>
using namespace std::chrono;
const int limit = 200;
const std::string factorial(int n)
{
	std::string res(limit, '0');
	res[0] = '1';
	for (int j = 1; j <= n; ++j)
	{
		int carry = 0;
		for (int i = 0; i < limit; ++i)
		{
			int product = (res[i] - '0')*j + carry;
			res[i] = '0' + (product % 10);
			carry = product / 10;
		}
	}
	
	std::reverse(res.begin(), res.end());
	res.erase(0, res.find_first_not_of('0'));
	return res;
}

int main()
{
	int n = 100;
	auto begin = system_clock::now();
	std::string f = factorial(n);
	std::cout << f << '\n';
	auto end = system_clock::now();
	auto elapsed = duration_cast<milliseconds>(end - begin);
	std::cout << "Time elapsed: " << elapsed.count() << '\n';
	return 0;
}