T = int(input())

C = 10 ** 6
dat = [0] * C
prime = []
for i in range(2,C):
    if dat[i] == 0:
        prime.append(i)
        for j in range(2 * i,C,i):
            dat[j] = 1
from collections import defaultdict

for _ in range(T):
    X = int(input())
    d = defaultdict(int)
    P = -1
    u = X
    for p in prime:
        if X % p != 0:
            P = p
            break
        while X % p == 0:
            d[p] += 1
            X //= p
    num = 1
    for v in d.values():
        num *= (v + 1)
    for j in range(2,p+1):
        div = 1
        t = j
        for k in prime:
            if k > p:break
            count = 0
            while j % k == 0:
                count += 1
                j //= k
            div *= (d[k] + 1 + count)
        if div == 2 * num:
            print(t * u)
            break