#include <cstring>
#include <algorithm>
#include <iostream>
#include <vector>
#include <cstdio>
using namespace std;
typedef long long LL;
const int N = 10010 ;
LL a , b, k;

vector<LL>f1,f2;

void cal()
{
    for(LL i = 1; i * i <= a ; ++i ){
        if( a % i == 0 ){
            if(  b % i == 0 ){
                f1.push_back(i);
            }
            LL temp = a / i ;
            if( temp != i && b % temp == 0 ){
                f2.push_back( temp );
            }
        }
    }
}

int main()
{
    #ifdef LOCAL
        freopen("in.txt","r",stdin);
    #endif // LOCAL
    int cas =1 , _;
    scanf("%d",&_);
    while(_--)
    {
        scanf("%I64d%I64d%I64d",&a,&b,&k);
        if( a > b ){
            swap(a , b);
        }
        f1.clear();
        f2.clear();
        cal();
        int len1 = (int ) f1.size() ,len2 = (int )f2.size();
        if( len1 + len2 < k )
            puts("-1");
        else{
            if( k <= len2 )
                printf("%I64d\n",f2[ k - 1 ]);
            else {
                k -= len2 ;
                printf("%I64d\n",f1[len1-k]);
            }
        }
    }
    return 0;
}