Find the first natural number whose factorial is divisible by x in C++

We have to find the first natural number whose factorial is divisible by x. The x is given by the user. So if the x = 16, then output will be 6. as 6! mod 16 = 0. We will use general approach to solve this problem. iteratively count 1!, 2!, …. n! and check divisibility using x. If modulus is 0, then stop and return the number.

Example

#include<iostream>
using namespace std;
int getNumber(int x) {
   int fact = 1;
   int i = 0;
   while(fact % x != 0){
      i++;
      fact = fact * i;
   }
   return i;
}
int main() {
   int x = 16;
   cout << "Minimum value of N is: " << getNumber(x);
}

Output

Minimum value of N is: 6