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;

class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int x = sc.nextInt();
        int y = sc.nextInt();
        /*xとyの最大公約数はyとx%yの最大公約数と同じなのでx%y==0になるまで入れ替えればyが最大公約数となる*/
        while(x%y!=0){
            int tmp = x%y; //tmpに一時的にx%yを格納し入れ替え
            x = y;
            y = tmp;
        }
        System.out.println(y);
    }
}