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) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner scan = new Scanner(System.in);
		int  x=scan.nextInt();
		int  y=scan.nextInt();
		int  Z=0;
		if (x>=y) {
			while(true) {
				Z=x % y;
				if (Z==0) break;
				else {
					x = y;
				    y = Z;
					
				}
			}
			System.out.println(y);
		}
		else {
			while(true) {
				Z=y % x ;
				if (Z==0) break;
				else {
					y = x;
				    x = Z;
					
				}
			}
			System.out.println(x);
		}
	}
}