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 C# (judge verdict: Accepted)

using static System.Console;

namespace AOJ
{
    public class ALDS1_1_B
    {
        public static void Main(string[] args)
        {
            string[] input = ReadLine().Split(' ');
            int a = int.Parse(input[0]);
            int b = int.Parse(input[1]);

            WriteLine(GreatestCommonDivisor(a,b));
        }

        /// <summary>
        /// The prerequisite: x > 0 , y > 0 
        /// Output: 0 ~ Min(x, y)
        /// </summary>
        public static int GreatestCommonDivisor(int x, int y)
        {
            if (x <= 1 || y <= 1) return 0;
            
            int divisor= x > y ? y : x;

            for (int i = divisor; i > 0; i--)
            {
                if (x % i == 0 && y % i == 0)
                {
                    return i;
                }
            }

            return 1;
        }
    }
}