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) throws Exception {

		Scanner scanner = new Scanner(System.in);// ??\?????????????????????
		
		int num01 = scanner.nextInt();
		int num02 = scanner.nextInt();
		int min = Math.min(num01, num02);
		int max = Math.max(num01, num02);
		int gcd = 1;// ?????§??¬?´???°???????´????????????°
		int surplus = 1;
		
		while(true){
			surplus = max % min;
			max = min;
			min = surplus;
			if(surplus == 0){
				break;
			}
		}
		System.out.println(max);// ?????§??¬?´???°?????????
	}
}