Find the GCD of all the non-prime numbers of given Array

Last Updated : 10 May, 2022

Given an array arr[] having N integers, the task is to find the GCD of all the numbers in the array which are not prime. If all the numbers are prime return -1.

Examples:

Input: N = 3, arr[ ] = {2, 3, 5}
Output: -1
Explanation: All the numbers are prime.
Hence answer will be -1.

Input: N = 6, arr[ ] = { 2, 4, 6, 12, 3, 5 }
Output: 2
Explanation: Non-prime numbers present in the array are 4, 6, and 12.
Their GCD is 2.

Approach: This problem can be solved by finding the prime numbers in the array using the Sieve of Eratosthenes.

Follow the below steps to solve the problem:

Find all the prime numbers in the range of minimum of the array and maximum of the array using the sieve Of Eratosthenes.
Now iterate through the given array and find the non-prime numbers.
Take GCD of all the non-prime numbers.

Below is the implementation of the above approach:

C++

// C++ code to implement the approach

#include <bits/stdc++.h>
using namespace std;

vector<int> isPrime(100001, 1);

// Function to find the prime numbers
void sieve(int n)
{
    // Mark 0 and 1 as non-prime
    isPrime[0] = 0;
    isPrime[1] = 0;

    // Mark all multiples of 2 as
    // non-prime
    for (int i = 4; i <= n; i += 2)
        isPrime[i] = 0;

    // Mark all non-prime numbers
    for (int i = 3; i * i <= n; i++) {
        if (isPrime[i]) {
            for (int j = i * i; j <= n;
                 j += i)
                isPrime[j] = 0;
        }
    }
}

// Find the GCD of the non-prime numbers
int nonPrimeGCD(vector<int>& arr, int n)
{
    int i = 0;

    // Find all non-prime numbers till n
    // using sieve of Eratosthenes
    sieve(n);

    // Find first non - prime number
    // in the array
    while (isPrime[arr[i]] and i < n)
        i++;

    // If not found return -1
    if (i == n)
        return -1;

    // Initialize GCD as the first
    // non prime number
    int gcd = arr[i];

    // Take gcd of all non-prime numbers
    for (int j = i + 1; j < n; j++) {
        if (!isPrime[arr[j]])
            gcd = __gcd(gcd, arr[j]);
    }
    return gcd;
}

// Driver code
int main()
{
    int N = 6;
    vector<int> arr = { 2, 4, 6, 12, 3, 5 };

    // Find non Prime GCD
    cout << nonPrimeGCD(arr, N);
    return 0;
}

Java

// Java code to implement the approach
import java.io.*;

class GFG {
  static int gcd(int a, int b)
  {
    if (b == 0)
      return a;
    return gcd(b, a % b);
  }

  static int[] isPrime = new int[100001];

  // Function to find the prime numbers
  public static void sieve(int n)
  {
    for (int i = 0; i <= n; i++) {
      isPrime[i] = 1;
    }
    // Mark 0 and 1 as non-prime
    isPrime[0] = 0;
    isPrime[1] = 0;

    // Mark all multiples of 2 as
    // non-prime
    for (int i = 4; i <= n; i += 2)
      isPrime[i] = 0;

    // Mark all non-prime numbers
    for (int i = 3; i * i <= n; i++) {
      if (isPrime[i] != 0) {
        for (int j = i * i; j <= n; j += i)
          isPrime[j] = 0;
      }
    }
  }

  // Find the GCD of the non-prime numbers
  public static int nonPrimeGCD(int arr[], int n)
  {
    int i = 0;

    // Find all non-prime numbers till n
    // using sieve of Eratosthenes
    sieve(n);

    // Find first non - prime number
    // in the array
    while (isPrime[arr[i]] != 0 && i < n)
      i++;

    // If not found return -1
    if (i == n)
      return -1;

    // Initialize GCD as the first
    // non prime number
    int gg = arr[i];

    // Take gcd of all non-prime numbers
    for (int j = i + 1; j < n; j++) {
      if (isPrime[arr[j]] == 0)
        gg = gcd(gg, arr[j]);
    }
    return gg;
  }

  // Driver Code
  public static void main(String[] args)
  {
    int N = 6;
    int arr[] = { 2, 4, 6, 12, 3, 5 };

    // Find non Prime GCD
    System.out.print(nonPrimeGCD(arr, N));
  }
}

// This code is contributed by Rohit Pradhan

Python3

# python3 code to implement the approach
import math

isPrime = [1 for _ in range(1000011)]

# Function for __gcd
def __gcd(a, b):
    if b == 0:
        return a
    return __gcd(b, a % b)

# Function to find the prime numbers
def sieve(n):
    global isPrime
    
    # Mark 0 and 1 as non-prime
    isPrime[0] = 0
    isPrime[1] = 0

    # Mark all multiples of 2 as
    # non-prime
    for i in range(4, n+1, 2):
        isPrime[i] = 0

        # Mark all non-prime numbers
    for i in range(3, int(math.sqrt(n)) + 1):
        if (isPrime[i]):
            for j in range(i*i, n+1, i):
                isPrime[j] = 0

# Find the GCD of the non-prime numbers
def nonPrimeGCD(arr, n):
    i = 0

    # Find all non-prime numbers till n
    # using sieve of Eratosthenes
    sieve(n)

    # Find first non - prime number
    # in the array
    while (isPrime[arr[i]] and i < n):
        i += 1

    # If not found return -1
    if (i == n):
        return -1

    # Initialize GCD as the first
    # non prime number
    gcd = arr[i]

    # Take gcd of all non-prime numbers
    for j in range(i+1, n):
        if (not isPrime[arr[j]]):
            gcd = __gcd(gcd, arr[j])

    return gcd

# Driver code
if __name__ == "__main__":

    N = 6
    arr = [2, 4, 6, 12, 3, 5]

    # Find non Prime GCD
    print(nonPrimeGCD(arr, N))

    # This code is contributed by rakeshsahni

// C# program for above approach
using System;
class GFG
{

  static int gcd(int a, int b)
  {
    if (b == 0)
      return a;
    return gcd(b, a % b);
  }

  static int[] isPrime = new int[100001];

  // Function to find the prime numbers
  public static void sieve(int n)
  {
    for (int i = 0; i <= n; i++) {
      isPrime[i] = 1;
    }
    // Mark 0 and 1 as non-prime
    isPrime[0] = 0;
    isPrime[1] = 0;

    // Mark all multiples of 2 as
    // non-prime
    for (int i = 4; i <= n; i += 2)
      isPrime[i] = 0;

    // Mark all non-prime numbers
    for (int i = 3; i * i <= n; i++) {
      if (isPrime[i] != 0) {
        for (int j = i * i; j <= n; j += i)
          isPrime[j] = 0;
      }
    }
  }

  // Find the GCD of the non-prime numbers
  public static int nonPrimeGCD(int[] arr, int n)
  {
    int i = 0;

    // Find all non-prime numbers till n
    // using sieve of Eratosthenes
    sieve(n);

    // Find first non - prime number
    // in the array
    while (isPrime[arr[i]] != 0 && i < n)
      i++;

    // If not found return -1
    if (i == n)
      return -1;

    // Initialize GCD as the first
    // non prime number
    int gg = arr[i];

    // Take gcd of all non-prime numbers
    for (int j = i + 1; j < n; j++) {
      if (isPrime[arr[j]] == 0)
        gg = gcd(gg, arr[j]);
    }
    return gg;
  }

// Driver Code
public static void Main()
{
    int N = 6;
    int[] arr = { 2, 4, 6, 12, 3, 5 };

    // Find non Prime GCD
    Console.Write(nonPrimeGCD(arr, N));
}
}

// This code is contributed by code_hunt.

JavaScript

<script>

// JavaScript code to implement the approach
let isPrime = new Array(100001).fill(1)

// Function to find the prime numbers
function sieve(n)
{
    // Mark 0 and 1 as non-prime
    isPrime[0] = 0;
    isPrime[1] = 0;

    // Mark all multiples of 2 as
    // non-prime
    for (let i = 4; i <= n; i += 2)
        isPrime[i] = 0;

    // Mark all non-prime numbers
    for (let i = 3; i * i <= n; i++) {
        if (isPrime[i]) {
            for (let j = i * i; j <= n;
                 j += i)
                isPrime[j] = 0;
        }
    }
}

function GCD(x,y){
    if (!y) {
        return x;
    }
    
      return GCD(y, x % y);
}

// Find the GCD of the non-prime numbers
function nonPrimeGCD(arr,n)
{
    let i = 0;

    // Find all non-prime numbers till n
    // using sieve of Eratosthenes
    sieve(n);

    // Find first non - prime number
    // in the array
    while (isPrime[arr[i]] && i < n)
        i++;

    // If not found return -1
    if (i == n)
        return -1;

    // Initialize GCD as the first
    // non prime number
    let gcd = arr[i];

    // Take gcd of all non-prime numbers
    for (let j = i + 1; j < n; j++) {
        if (!isPrime[arr[j]])
            gcd = GCD(gcd, arr[j]);
    }
    return gcd;
}

// Driver code
let N = 6
let arr = [ 2, 4, 6, 12, 3, 5 ]

// Find non Prime GCD
document.write(nonPrimeGCD(arr, N))

// This code is contributed by shinjanpatra

</script>

Output

Time Complexity: O(N * log(log( N )))
Auxiliary Space: O(N)

Find the GCD of an array made up of numeric strings

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