mod = 1000000007
eps = 10**-9


def main():
    import sys
    input = sys.stdin.readline

    def PrimeDecomposition(N):
        ret = {}
        n = int(N ** 0.5)
        for d in range(2, n + 1):
            while N % d == 0:
                if d not in ret:
                    ret[d] = 1
                else:
                    ret[d] += 1
                N //= d
            if N == 1:
                break
        if N != 1:
            ret[N] = 1
        return ret

    def euler_phi(N):
        P = PrimeDecomposition(N)
        ret = N
        for p in P:
            ret = ret * (p-1) // p
        return ret

    for _ in range(int(input())):
        N = int(input())
        if N == 1:
            print(1)
            continue
        phi = euler_phi(2 * N - 1)
        div = []
        for i in range(1, phi + 1):
            if i * i > phi:
                break
            if phi % i == 0:
                div.append(i)
                div.append(phi // i)
        div.sort()
        for d in div:
            if pow(2, d, 2*N-1) == 1:
                print(d)
                break


if __name__ == '__main__':
    main()