Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
class Hjo {
  static void Main(){
    var aho = Console.ReadLine().Split();
    var a = int.Parse(aho[0]);
    var b = int.Parse(aho[1]);
    var K = int.Parse(aho[2]);
    var sore = 0;
    var syou = 0;
    var numbers = new List<int>();
    if(a > b){
      syou = b;
    }
    else{
      syou = a;
    }
    for(var i = 1;i <= syou;i++){
         if(a%i == 0&&b%i==0){
			numbers.Add(i);
         }
    }
    var kotae = numbers.OrderByDescending(x=> x).ToList();
        Console.WriteLine(kotae[K-1]);
    
   
  }
}