Primes_MAX = 10 ** 4
Primes = []
Sieve = [0] * Primes_MAX
Sieve[0] = Sieve[1] = -1
for p in range(2, Primes_MAX):
    if not Sieve[p]:
        Primes.append(p)
        Sieve[p] = p
        for q in range(p * p, Primes_MAX, p):
            if not Sieve[q]:
                Sieve[q] = p

def factorize(x):
    ret = []
    while x != 1:
        p = Sieve[x]
        cnt = 0
        while x % p == 0:
            x //= p
            cnt += 1
        ret.append((p, cnt))
    return ret

for _ in range(int(input())):
    x = int(input())
    for i in range(2, Primes_MAX):
        fs = factorize(i)
        pre = 1
        for p, _ in fs:
            cnt = 0
            tmp = x
            while tmp % p == 0:
                tmp //= p
                cnt += 1
            pre *= 1 + cnt
        y = x * i
        nxt = 1
        for p, _ in fs:
            cnt = 0
            tmp = y
            while tmp % p == 0:
                tmp //= p
                cnt += 1
            nxt *= 1 + cnt
        if 2 * pre == nxt:
            print(y)
            break