#include <iostream>
#include <string>
#include <cmath>
#include <cstring>
#include <set>
typedef __int64 ll;
using namespace std;

set<ll> s;
ll GCD(ll xx,ll yy)
{
    ll r=1;
    while(r!=0)
    {
        r=xx%yy;
        xx=yy;
        yy=r;
    }
    return xx;
}

int main()
{
    int T;
    ll x,y,k,gcd,count;
    cin>>T;
    while(T--)
    {
        count=0;
        cin>>x>>y>>k;
        gcd=GCD(x,y);
        for(int i=1;i<=sqrt(gcd);i++)
        {
            if(gcd%i==0)
            {
                s.insert(i);
                s.insert(gcd/i);
            }
        }
        set<ll>::reverse_iterator rit;
        for(rit=s.rbegin();rit!=s.rend();rit++)
        {
            //cout<<*rit<<" ";
            count++;
            if(count==k)
            {
              cout<<*rit<<endl;
              break;
            }
        }
        if(count<k)cout<<"-1"<<endl;
        s.clear();
    }
    return 0;
}

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