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 x = sc.nextInt();
		int y = sc.nextInt();

		System.out.println(euclideanAlgorithm(x, y));
	}

	public static int euclideanAlgorithm(int x, int y) {
		int tmp;
		while (true) {
			tmp = x % y;
			if (tmp == 0) {
				return y;
			}
			x = y;
			y = tmp;
		}
	}
}