#include<cstdio>
#include<cstring>
#include<algorithm>
#include<math.h>
#include<queue>
#include<iostream>
using namespace std;
typedef long long LL;
LL gcd(LL a,LL b){
    return b==0?a:gcd(b,a%b);
}
LL p[10005];
LL cmp(LL a,LL b){
    return a>b;
}
int main()
{
    int tcase;
    scanf("%d",&tcase);
    while(tcase--){
        LL a,b,k;
        scanf("%lld%lld%lld",&a,&b,&k);
        LL d = gcd(a,b);
        int id = 0;
        for(LL i=1;i*i<=d;i++){ ///筛选出所有因子
            if(d%i==0){
                 if(i*i==d) p[id++]=i;
                 else{
                    p[id++]=i;
                    p[id++]=d/i;
                 }
            }
        }
        if(id<k){
            printf("-1\n");
        }
        else{
            sort(p,p+id,cmp);
            printf("%lld\n",p[k-1]);
        }
    }
    return 0;
}