# Absolute Difference between the Product of Non-Prime numbers and Prime numbers of an Array?

Here we will see how we can find the absolute difference between the product of all prime numbers and all non-prime numbers of an array. To solve this problem, we have to check whether a number is prime or not. One possible way for primality testing is by checking a number is not divisible by any number between 2 to square root of that number. So this process will take 𝑂(√𝑛) amount of time. Then get the product and try to find the absolute difference.

## Algorithm

#### diffPrimeNonPrimeProd(arr)

begin
prod_p := product of all prime numbers in arr
prod_np := product of all non-prime numbers in arr
return |prod_p – prod_np|
end

## Example

Live Demo

#include <iostream>
#include <cmath>
using namespace std;
bool isPrime(int n){
for(int i = 2; i<=sqrt(n); i++){
if(n % i == 0){
return false; //not prime
}
}
return true; //prime
}
int diffPrimeNonPrimeProd(int arr[], int n) {
int prod_p = 1, prod_np = 1;
for(int i = 0; i<n; i++){
if(isPrime(arr[i])){
prod_p *= arr[i];
} else {
prod_np *= arr[i];
}
}
return abs(prod_p - prod_np);
}
main() {
int arr[] = { 4, 5, 3, 8, 13, 10};
int n = sizeof(arr) / sizeof(arr);
cout << "Difference: " << diffPrimeNonPrimeProd(arr, n);
}

## Output

Difference: 125