#include <bits/stdc++.h>
using namespace std;
typedef  long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<ll> vll;
int inf_int=2e9;
ll inf_ll=2e18;
typedef pair<int,int> pii;
#define pb push_back
const double pi=3.1415926535898;
#define dout if(debug) cout
#define fi first
#define se second
#define sp setprecision
#define sz size()


#define x1 gfgs
#define y1 asd
#define rank asdsad
bool debug=0;
const int maxn=5e5+107;
ll mod=1e9+7;



void solve()
{
    int n;
    cin >> n;
    int a[n];
    for(int i=0;i<n;i++)
    {
        cin >> a[i];
    }
    if(n==2)
    {
        cout << min(a[0],a[1])<<"\n";
        return;
    }
    int ans=1;
    int x=a[0];
    for(int i=1;i*i<=x;i++)
    {

        if(x%i==0)
        {
            int nod2=-1;
            for(int e=1;e<n;e++)
            {
                if(a[e]%i==0)
                {
                    continue;
                }
                else
                {
                    if(nod2==-1)
                    {
                        nod2=a[e];
                    }
                    else
                    {
                        nod2=__gcd(nod2,a[e]);
                    }
                    if(nod2<ans)
                        break;
                }
            }
            if(nod2==-1)
            {
                nod2=i;
            }
            ans=max(ans,min(nod2,i));

            int del=x/i;
            nod2=-1;
            for(int e=1;e<n;e++)
            {
                if(a[e]%del==0)
                {
                    continue;
                }
                else
                {
                    if(nod2==-1)
                    {
                        nod2=a[e];
                    }
                    else
                    {
                        nod2=__gcd(nod2,a[e]);
                    }
                    if(nod2<ans)
                        break;
                }
            }
            if(nod2==-1)
            {
                nod2=del;
            }
            ans=max(ans,min(nod2,del));
        }
    }
    cout << ans<<"\n";

}


#define FILE "bridges"
int main()
{

       // freopen("a.txt","r",stdin);
       // freopen("output.txt","w",stdout);

      //   freopen(FILE".in","r",stdin);
      //   freopen(FILE".out","w",stdout);
       if(!debug)
       {
            ios_base::sync_with_stdio(0);
            cin.tie(0);
           cout.tie(0);
       }
        int t=1;
        cin >> t;
        while(t--)
            solve();
        return 0;
}