E0079.cpp

// Problem Code: LEDIV

#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>

using namespace std;

int size = pow(10, 5);
vector<int> leastPrime(size + 1, 0);

void modifiedSieveOfEratosthenes() {
	int i, j;
	leastPrime[1] = 1;
	for (i = 2; i * i <= size; i++)
		if (leastPrime[i] == 0) {
			leastPrime[i] = i;
			for (j = 2 * i; j <= size; j += i)
				if (leastPrime[j] == 0)
					leastPrime[j] = i;
		}
	for (; i <= size; i++)
		if (leastPrime[i] == 0)
			leastPrime[i] = i;
}

int littleElephantAndDivisors(vector<int> A) {
	int x, gcd = A[0];
	for (int i=1 ; i < A.size() ; i++)
			gcd = __gcd(A[i], gcd);
	return leastPrime[gcd];
}

int main() {
	modifiedSieveOfEratosthenes();
	leastPrime[1] = -1;
	int T;
	cin >> T;
	while (T--) {
			int N;
			cin >> N;
			vector<int> A(N);
			for (int i=0 ; i < N ; i++)
					cin >> A[i];
			cout << littleElephantAndDivisors(A) << endl;
	}
	return 0;
}