#pragma GCC optimize("O3,unroll-loops,Ofast")
// #pragma GCC target("avx2")
#include<bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
#define int long long
#define endl '\n'
using namespace std;
using pii = pair<int, int>;
using tup = tuple<int, int, int>;
// mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// template <class T> using ordered_set = tree<T, null_type,
// less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const int inf = (1e15)+5;
const int mod = 1000000007;
const double eps = 1e-6;
const int N = 100002;
vector<int> divs[N];
void preprocess() {
for (int i = 1; i < N; i++) {
for (int j = i; j < N; j += i) {
divs[j].push_back(i);
}
}
}
int n, a[N];
int cnt[N];
int calc(int x) {
int tot = 0, out = 0;
for(int i=1; i<=n; i++) {
if(a[i] % x == 0) tot++;
else out = gcd(out, a[i]);
}
int onno = n - tot;
int lage;
if(n % 2 == 0) {
if(tot < n/2) return 0;
lage = n / 2;
}
else {
if(tot >= n/2+1) lage = n/2;
else if(tot == n/2) lage = n/2+1;
else return 0;
}
lage -= onno;
for(int i=1; i<=n; i++) {
if(a[i] % x) continue;
for(int j : divs[a[i]/x])
cnt[j]++;
}
// cout << tot << ' ' << onno << ' ' << lage << ' ' << out << endl;
int ret = 0;
for(int i=1; i<N; i++) {
if(out % i or cnt[i] < lage) continue;
ret = max(ret, i);
}
for(int i=1; i<=n; i++) {
if(a[i] % x) continue;
for(int j : divs[a[i]/x])
cnt[j]--;
}
if(out % x == 0) ret *= x;
// cout << x << ": " << ret + x << endl;
return ret + x;
}
void solve(int tc) {
cin >> n;
for(int i=1; i<=n; i++) cin >> a[i];
int ans = 0;
for(int i : divs[a[1]]) ans = max(ans, calc(i));
cout << ans << endl;
}
int32_t main() {
cin.tie(NULL)->sync_with_stdio(false);
cout.precision(10);
preprocess();
int T = 1;
cin >> T;
for (int i = 1; i <= T; i++) {
solve(i);
}
return 0;
}