Finding the power of prime number p in n! in C++

In this problem, we are given a number n and a prime number p. Our task is to find the power of prime number p in n!

Let's take an example to understand the problem,

Input : n = 6, p = 2
Output : 4

Solution Approach

A simple solution to the problem is by simply finding the values of n!. And the factorize it, and find the power of prime number p in the factorization.

Here, the number can be represented as the power factorization of 2 in 5! = 30 is 3.

The value of n factorial is

$$n!\:=\:n^*(n-1)^*(n-2)^*(n-3)\dotso{^*}2^*1$$ 

$$n!\:=\:3^*2^*1\:=\:6$$

Let take n = 6 and p = 2,

n! = 6! = (2*3*4*5*6)

n! = 720

Factorisation of 720 is 2*2*2*2*3*3*5

The power of 2 in the factorisation of 6! is 4.

Hence the output is 4.

Example

Program to illustrate the working of our solution

#include <iostream>
using namespace std;
int powerOfPrimeNfactorial(int N, int P){
   int primePower = 0;
   int factVal = P;
   while (factVal <= N) {
      primePower += N / factVal;
      factVal = factVal * P;
   }
   return primePower;
}
int main(){
   int N = 6;
   int P = 2;
   cout<<"The power of prime number "<<P<<" in "<<N<<"! is "<<powerOfPrimeNfactorial(N, P) << endl;
   return 0;
}

Output

The power of prime number 2 in 6! is 4