Problem:
Greatest Common Divisor

Write a program which finds the greatest common divisor of two natural numbers a and b

Input

a and b are given in a line sparated by a single space.

Output

Output the greatest common divisor of a and b.

Constrants

1 ≤ a, b ≤ 109

Hint

You can use the following observation:

For integers x and y, if x ≥ y, then gcd(x, y) = gcd(y, x%y)

Sample Input 1

54 20

Sample Output 1

2

Sample Input 2

147 105

Sample Output 2

21

Solution in JAVA (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in); 

		int a = sc.nextInt();
		int b = sc.nextInt();
		
		int x = Math.max(a, b);
		int y = Math.min(a, b);
		
		for (int mod = x % y; mod != 0; x = y, y = mod, mod = x % y) {
			
		}
		
    	System.out.println(y);
    	
        sc.close();
	}
}