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 int euclidean(int x, int y) {
		int result = -1, z = 1;
		while (z > 0) {
			z = x % y;
			if (z == 0) result = y;
			x = y; y = z;
		}
		return result;
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int x = sc.nextInt();
		int y = sc.nextInt();
		if (y > x ) {
			int tmp = x; x = y; y = tmp;
		}
		int factor = euclidean(x, y);
		if (factor == -1) {
			System.out.println("not exist Greatest common factor");
		} else {
			System.out.println(euclidean(x, y));
		}
	}
}