Java Program for Extended 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

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

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

class GFG {
     static  public void gcdExtended(long a, long b)
    {
        long x = 0, y = 1, lastx = 1, lasty = 0, temp;
        while (b != 0)
        {
            long q = a / b;
            long r = a % b;

            a = b;
            b = r;

            temp = x;
            x = lastx - q * x;
            lastx = temp;

            temp = y;
            y = lasty - q * y;
            lasty = temp;
        }
      System.out.println("GCD "+a+" and its Roots  x : "+ lastx +" y :"+ lasty);

    }

    // Driver Program
    public static void main(String[] args)
    {

        long a = 35, b = 15;
      //this will print result like
      //Roots  x : 1 y :-2
      gcdExtended(a, b);

    }
}
// Code Contributed by Aryan itsmearyan <(0-o)>

Output:

gcd(35, 15) = 5

Please refer complete article on Basic and Extended Euclidean algorithms for more details!