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 {
	Scanner sc = new Scanner(System.in);
	int x,y;	
	int keep=0;
	
	public void input() {
		x = sc.nextInt();
		y = sc.nextInt();
	}
	
	public void conpute() {
		if(x > y) {
			while(x%y != 0) {
				keep = x;
				x = y;
				y = keep % y;
			}
			System.out.println(y);
		}else {
			while(y%x != 0) {
				keep = y;
				y = x;
				x = keep % y;
			}
			System.out.println(x);
		}
	}
	
	public static void main(String[] args) {
		Main obj = new Main();
		obj.input();
		obj.conpute();
	}
}