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 scan = new Scanner(System.in);
		long x = scan.nextLong();
		long y = scan.nextLong();
		scan.close();
		long smaller = Math.min(x, y);
		long bigger = Math.max(x, y);
		System.out.println(GreatestCommonDivisor(bigger, smaller));
	}

	static long GreatestCommonDivisor(long x, long y){
		long mod = Math.floorMod(x, y);
		if(mod == 0){
			return y;
		}else{
			x = Math.max(y, mod);
			y = Math.min(y, mod);
			return GreatestCommonDivisor(x, y);
		}
	}
}