input = 5;
5! = 5(4)(3)(2)(1)

#include <iostream>

using namespace std;

int main()
{
    int fac = 0;
    int sum = 0;
    int cnt = 1;
    cout << "Input a number to get the Factorial: ";
    cin >> fac;

    for (fac; fac > 0; cnt ++)
    {
        sum = fac(fac - cnt)
    }

    cout << fac << "! : ";
}

sum = fac * (fac - cnt)

for( fac; fac > 0; cnt++ )
{
    sum = fac * (fac - cnt);
}

int prod = 1;
for( i = fac; i > 0; --i ) // <-- notice the --i
    prod = prod * i;       // <-- equiv to prod *= i;

prod      i       new_prod
---------------------------
  1       5        1*5 = 5
  5       4        5*4 = 20
 20       3       20*3 = 60
 60       2       60*2 = 120
 120      1      120*1 = 120
 120

cout << fac << "! = " << prod << endl;

int fac(int n)
{
  return (n == 1 || n == 0) ? 1 : fac(n - 1) * n;
}