#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>
using namespace std;
vector<long long> s;
long long gcd(long long a,long long b)
{
    return b==0?a:gcd(b,a%b);
}
int main()
{
    long long x,y,k;
    int t;
    scanf("%d",&t);
    while(t--)
    {
        s.clear();
        scanf("%I64d%I64d%I64d",&x,&y,&k);
        long long u=gcd(x,y);
        for(long long i=1;i*i<=u;i++)
        {
            if(u%i==0)
            {
              s.push_back(i);
              if(i*i!=u)
              s.push_back(u/i);
            }
        }
        if(s.size()<k)
        {
            printf("-1\n");
        }
        else
        {
            sort(s.begin(),s.end());
            printf("%I64d\n",s[s.size()-k]);
        }
    }
    return 0;
}