//karanaggarwal
#include<bits/stdc++.h>
using namespace std;

#define TRACE
#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
#else
#define trace(...)
#endif

#define si(x) scanf("%d",&x)
#define sll(x) scanf("%lld",&x)
#define pi(x) printf("%d\n",x)
#define F first
#define S second
#define PB push_back
#define MP make_pair
#define LET(x,a) __typeof(a) x(a)
#define TR(v,it) for( LET(it,v.begin()) ; it != v.end(); it++)

typedef long long LL;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<PII> VPII;

const int mod = 1000000007;
LL gcd(LL a, LL b){ if(b)return gcd(b,a%b); return a;}
VI primes;
const int N = 1000001;
bitset<N> P;

LL A[100];
int main(int argc, char** argv)
{

    P.set();
    for(int i =2; i*i<=1000000; i++)
        if(P[i]==true)
            for(int j = i*i; j<=1000000; j+=i)
                P[j] = false;
    for(int i =2; i<=1000000; i++) if(P[i]) primes.PB(i);
    int t; si(t); while(t--)
    {
        int n; si(n); 
        for(int i =0; i<n; i++) sll(A[i]);
        LL g  = 1;
        for(int i =0; i<n; i++)
            for(int j = i+1; j<n; j++)
                if(gcd(A[i],A[j])!=1)
                {
                    g = gcd(A[i],A[j]); break;
                }
        for(int i =0; i<n and g==1; i++)
        {
            for(auto x : primes)
            {
                if(x > A[i])break;
                if(A[i] % x)continue; 
                A[i]/=x;
                if(A[i]%x==0){
                    g = x; break;
                }
            }
            if(g==1){
                LL r = sqrt(A[i]); 
                while(r*r > A[i])r--; 
                while(r*r < A[i])r++;
                if(r*r==A[i])
                    g = r;
            }
        }
//        assert(g!=1);
        cout<<g<<endl;
    }
    return 0;	
}