Question

JAVA CLASS

Greatest Common Divisor Finder

Enter first number: 12

Enter second number: 8

Greatest common divisor: 4

Continue? (y/n): y

Enter first number: 77

Enter second number: 33

Greatest common divisor: 11

Continue? (y/n): y

Enter first number: 441

Enter second number: 252

Greatest common divisor: 63

Continue? (y/n): n

The formula for finding the greatest common divisor of two positive integers x and y follows the Euclidean algorithm as follows:

1.   Subtract x from y repeatedly until y < x.
2.   Swap the values of x and y.
3.   Repeat steps 1 and 2 until x = 0.
4.   y is the greatest common divisor of the two numbers.

You can use one loop for step 1 of the algorithm nested within a second loop for step 3.

Assume that the user will enter valid integers for both numbers.

The application should continue only if the user enters 'y' or 'Y' to continue.

Answer 1

//GCDFinder.java
import java.util.Scanner;
public class GCDFinder {
    public static void main(String[] args) {
        int a, b, t;
        Scanner scanner = new Scanner(System.in);
        char ch = 'y';

        System.out.println("Greatest Common Divisor Finder");
        while (ch=='y') {
            System.out.print("Enter first number: ");
            a = scanner.nextInt();
            System.out.print("Enter second number: ");
            b = scanner.nextInt();

            if (b > a) {
                t = a;
                a = b;
                b = t;
            }

            while (b != 0) {
                t = b;
                b = a % t;
                a = t;
            }

            System.out.println("Greatest common divisor: " + a);

            System.out.print("Continue? (y/n): ");
            ch = scanner.next().charAt(0);
        }
    }
}