#include<bits/stdc++.h>
#define ll long long
#define ios ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#pragma GCC optimize("O3","unroll-loops")
#pragma GCC optimize("Ofast")
using namespace std;
ll check(ll n) {
    ll l=-1;
    while(n%2==0)
    {
        l=2;
        n/=2;
    }
    for(int i=3;i<=sqrt(n);i+=2)
    {
        while (n % i == 0) {
            l = i;
            n /= i;
        }
    }
    if(n>2)
        l=n;
    return l;
}
int main()
{
    ll t;
    cin>>t;
    while(t--)
    {
        ll n;
        cin>>n;
        cout<<check(n)<<"\n";
    }
    return 0;
}