import java.util.Arrays;
import java.util.Scanner;
public class Prog {
public static void main(String[] args) {
// TODO Auto-generated method stub
Scanner s = new Scanner(System.in);
int t = s.nextInt();
while(t-->0)
{
int n = s.nextInt();
long a[]= new long[n];
for(int i=0;i<n;i++){
a[i] = s.nextLong();
}
Arrays.sort(a);
int flag = 0;
int value = -1;
//for(long disp:a)
// System.out.print(disp+" ");
for(int i=2;i<=a[0]/2;i++)
{
//System.out.println("Value of divisor is "+i);
flag = 0;
for(int j =0;j<n;j++)
{
if(a[j]%i == 0)
{
// System.out.println("a[j]%i == 0 True");
flag = 1;
}
else
{
// System.out.println("a[j]%i == 0 Not True");
flag = 0;
break;
}
}
if(flag == 1){
value = i;
break;
}
}
if(flag == 1){
System.out.println(value);
}
else
{
int obj = 0;
for(int j=0;j<n;j++){
if(a[j]% a[0] == 0){
obj =1;
}
else{
obj = 0;
break;
}
}
if(obj ==1)
{
if(a[0] == 1)
{
System.out.println(-1);
}
else
{
System.out.println(a[0]);
}
}
else
System.out.println(-1);
}
}
}
}