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# 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

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