Java Program for Basic Euclidean algorithms

GCD of two numbers is the largest number that divides both of them. A simple way to find GCD is to factorize both numbers and multiply common factors.

// Java program to demonstrate working of extended
// Euclidean Algorithm

import java.util.*;
import java.lang.*;

class GFG {
    // extended Euclidean Algorithm
    public static int gcd(int a, int b)
    {
        if (a == 0)
            return b;

        return gcd(b % a, a);
    }

    // Driver Program
    public static void main(String[] args)
    {
        int a = 10, b = 15, g;
        g = gcd(a, b);
        System.out.println("GCD(" + a + ", " + b + ") = " + g);

        a = 35;
        b = 10;
        g = gcd(a, b);
        System.out.println("GCD(" + a + ", " + b + ") = " + g);

        a = 31;
        b = 2;
        g = gcd(a, b);
        System.out.println("GCD(" + a + ", " + b + ") = " + g);
    }
}
// Code Contributed by Mohit Gupta_OMG <(0_o)>

Output:

GCD(10, 15) = 5
GCD(35, 10) = 5
GCD(31, 2) = 1

Time Complexity: O(Log min(a, b))
Please refer complete article on Basic and Extended Euclidean algorithms for more details!