#include<bits/stdc++.h>
using namespace std;
#define nl "\n"
#define fi first
#define se second
#define pb push_back
#define ll long long
#define ull unsigned ll
#define RV  return void
#define sz(x) int(x.size())
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define fixed(n) fixed << setprecision(n)
#define cin(v) for (auto&i:v) cin >> i;
#define cout(v) for (auto&i:v) cout << i << " ";
#define clr(memo, x) memset(memo, x, sizeof memo)
#define FastCode ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);

void  Zainab(){
            // #ifndef ONLINE_JUDGE
              // freopen("hobz.in", "r", stdin);
              // freopen("longpath.out", "w", stdout);
            // #endif
}


void myCode( ){

ll n ;
    cin >>n ;
    vector < ll > v(n) , pref(n+1,1 ) , suff(n+1,1);
    cin(v);

    for(int i=0 ; i < n ; i++){
        pref[i] = v[i];
        if(i) pref[i] = __gcd(pref[i-1] , pref[i]);
    }

    for(int i=n-1 ;i >=0 ; i--){
        suff[i] = v[i];
        if(i != n-1)
            suff[i] = __gcd(suff[i+1] , suff[i]);
    }

    ll ans=1;
    map < ll , ll > saved;
    for(int i =0; i < n ; i++){
        ll tx = suff[i+1];
        if(i)
            tx = pref[i-1];

        ll gc = __gcd( tx , suff[i+1])
        , gc2 = __gcd(v[i] , gc)
        , fin = gc/gc2
        , mx =1;


        if(saved[fin])
            mx = saved[fin];

        else{
            for(ll j =2 ; j*j <= fin ; j+= 1 + (j &  1)){
                if(fin % j == 0){
                    mx = max(mx , j);

                    while(fin % j ==0)
                        fin/=j;
                }
            }

            if( fin > 1)
                mx = max(mx , fin);
        }

        saved[gc/ gc2] = mx;
        ans = max(ans , __gcd(gc , mx*gc2));

            // cout << i << " " << gc << " " << gc2 << " " << mx << nl;
    }




    cout << ans << nl;


}


int main(){
                                   FastCode ;

    int testCase=1;
          cin >> testCase ;
      for(int i=1 ; i<= testCase ; i++)
        myCode();

    return 0;
}