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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
namespace Sample
{
  class Sample
  {
    static void Main(string[] args)
    {
    string[] str=Console.ReadLine().Split(' ');
      int A=int.Parse(str[0]);
      int B=int.Parse(str[1]);
      int K=int.Parse(str[2]);
      List<int> intList = new List<int>();
      
     for(int i=1;i<=Math.Min(A,B);i++){
      if(((A%i)==0)&&((B%i)==0)){
        
        intList.Add(i);
 
      }
     }
         int[] arr=intList.ToArray();
      Array.Sort(arr);
      Array.Reverse(arr);
      Console.WriteLine(arr[K-1]);
    }
    
  }

}