Check if two numbers are co-prime or not

Last Updated : 14 Oct, 2024

Two numbers A and B are said to be Co-Prime or mutually prime if the Greatest Common Divisor of them is 1. You have been given two numbers A and B, find if they are Co-prime or not.
Examples :

Input : 2 3
Output : Co-Prime

Input : 4 8
Output : Not Co-Prime

The idea is simple, we find GCD of two numbers and if GCD is 1, we return true, else false.

C++

// CPP program to check if two 
// numbers are co-prime or not
#include<bits/stdc++.h>
using namespace std;

// function to check and print if 
// two numbers are co-prime or not 
void coprime(int a, int b) {
    
    if ( __gcd(a, b) == 1)
        cout << "Co-Prime" << endl; 
    else
        cout << "Not Co-Prime" << endl;        
}

// driver code
int main()
{
    int a = 5, b = 6;
    coprime(a, b);    
    a = 8, b = 16;
    coprime(a, b);        
    return 0;
}

Java

// Java program to check if two 
// numbers are co-prime or not
import java.io.*;
public class GFG {
    
    // Recursive function to
    // return gcd of a and b
    static int __gcd(int a, int b)
    {
        // Everything divides 0 
        if (a == 0 || b == 0)
            return 0;
        
        // base case
        if (a == b)
            return a;
        
        // a is greater
        if (a > b)
            return __gcd(a-b, b);
                
        return __gcd(a, b-a);
    }
    
    // function to check and print if 
    // two numbers are co-prime or not 
    static void coprime(int a, int b) {
        
        if ( __gcd(a, b) == 1)
            System.out.println("Co-Prime"); 
        else
            System.out.println("Not Co-Prime");     
    }
    
    //driver code
    public static void main (String[] args)
    {
        int a = 5, b = 6;
        coprime(a, b); 
        
        a = 8; b = 16;
        coprime(a, b); 
    }
}

// This code is contributed by Anant Agarwal.

Python3

 
# Python3 program to check if two 
# numbers are co-prime or not

# Recursive function to
# return gcd of a and b
def __gcd(a, b):

    # Everything divides 0 
    if (a == 0 or b == 0): return 0
    
    # base case
    if (a == b): return a
    
    # a is greater
    if (a > b): 
        return __gcd(a - b, b)
            
    return __gcd(a, b - a)

# Function to check and print if 
# two numbers are co-prime or not 
def coprime(a, b):
    
    if ( __gcd(a, b) == 1):
        print("Co-Prime")
    else:
        print("Not Co-Prime")     

# Driver code
a = 5; b = 6
coprime(a, b) 

a = 8; b = 16
coprime(a, b)

# This code is contributed by Anant Agarwal

// C# program to check if two
// numbers are co-prime or not
using System;

class GFG {

    // Recursive function to
    // return gcd of a and b
    static int __gcd(int a, int b)
    {
        // Everything divides 0
        if (a == 0 || b == 0)
            return 0;

        // base case
        if (a == b)
            return a;

        // a is greater
        if (a > b)
            return __gcd(a - b, b);

        return __gcd(a, b - a);
    }

    // function to check and print if
    // two numbers are co-prime or not
    static void coprime(int a, int b) {

        if (__gcd(a, b) == 1)
            Console.WriteLine("Co-Prime");
        else
            Console.WriteLine("Not Co-Prime");
    }

    // Driver code
    public static void Main()
    {
        int a = 5, b = 6;
        coprime(a, b);
        a = 8;
        b = 16;
        coprime(a, b);
    }
}

// This code is contributed by Anant Agarwal.

JavaScript

<script>

// Javascript program to check if two
// numbers are co-prime or not

// Recursive function to
// return gcd of a and b
function __gcd(a, b)
{
    
    // Everything divides 0 
    if (a == 0 || b == 0)
        return 0;
    
    // Base case
    if (a == b)
        return a;
    
    // a is greater
    if (a > b)
        return __gcd(a - b, b);
            
    return __gcd(a, b - a);
}

// Function to check and print if 
// two numbers are co-prime or not 
function coprime(a, b)
{
    if (__gcd(a, b) == 1)
        document.write("Co-Prime" + "<br>"); 
    else
        document.write("Not Co-Prime");     
}


// Driver Code
var a = 5, b = 6;
coprime(a, b); 

a = 8; b = 16;
coprime(a, b); 

// This code is contributed by Kirti

</script>

PHP

<?php
// PHP program to check if two
// numbers are co-prime or not

// Recursive function to
// return gcd of a and b
function __gcd($a, $b)
    {
        // Everything divides 0
        if ($a == 0 || $b == 0)
            return 0;

        // base case
        if ($a == $b)
            return $a;

        // a is greater
        if ($a > $b)
            return __gcd($a - $b, $b);

        return __gcd($a, $b - $a);
    }

    // function to check and print if
    // two numbers are co-prime or not
function coprime($a, $b) 
{
    if (__gcd($a, $b) == 1)
        echo "Co-Prime","\n";
    else
        echo "Not Co-Prime","\n";
}

// Driver Code
$a = 5; $b = 6;
coprime($a, $b);
$a = 8;
$b = 16;
coprime($a, $b);

// This code is contributed by aj_36
?>

Output

Co-Prime
Not Co-Prime

Time Complexity: O(log(max(a,b)))

Auxiliary Space: O(1)

GCD of more than two (or array) numbers

Dibyendu Roy Chaudhuri

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Check if two numbers are co-prime or not

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