#include <bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define ld long double
#define be(a) a.begin(), a.end()
//#define l(x, n) for (int x = 0; x < n; ++x)
//#define f first
//#define s second
//#pragma GCC optimize("Ofast")
using namespace std;

void f(int x, int gcd1, vector <int> &a, vector <int> &q, map <int, int> &p, int &ans) {
    if (x == q.size()) {
        if (gcd1 <= ans)
            return;
        //cout << gcd1 << endl << endl;
        int gcd2 = 2e9;
        for (int i = 0; i < a.size() && gcd2 >= ans; ++i)
            if (a[i]%gcd1)
                gcd2 = gcd2 == 2e9? a[i] : __gcd(gcd2, a[i]);
        ans = max(ans, min(gcd1, gcd2));
    }
    else {
        int m = q[x], n = p[m], prod = 1;
        for (int i = 0; i <= n; ++i, prod *= m)
            f(x + 1, gcd1*prod, a, q, p, ans);
    }
}

int main() {
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int t;
    cin >> t;
    while (t--) {
        int n, m = 2e9, ans = 1;
        cin >> n;
        vector <int> a(n);
        for (int &i : a)
            cin >> i,
            m = min(m, i);
        int mm = m;
        map <int, int> p;
        vector <int> q;
        for (int i = 2; i*i <= m; ++i) {
            if (m%i == 0)
                q.push_back(i);
            while (m%i == 0)
                ++p[i],
                m /= i;
        }
        if (m != 1)
            ++p[m],
            q.push_back(m);
        f(0, 1, a, q, p, ans);
        cout << (ans == 2e9 ? mm : ans) << endl;
    }

    return 0;
}