#include <bits/stdc++.h>
#pragma GCC optimize("unroll-loops,no-stack-protector")
#pragma GCC target("sse,sse2,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
long long gcd(long long a, long long b) { return (!b ? a : gcd(b, a % b)); }
long long lcm(long long a, long long b) { return ((a * b) / gcd(a, b)); }
const long long MOD = 998244353;
const int INF32 = 1 << 30;
const long long INF64 = 1LL << 60;
const long double pi = 3.141592653589793;
long long modpow(long long n, long long k, long long mod) {
  if (k == 0) return 1;
  long long r = modpow(n * n % mod, k >> 1, mod);
  if (k & 1) r = r * n % mod;
  return r;
}
void solve() {
  int t;
  cin >> t;
  while (t--) {
    long long p, q;
    cin >> p >> q;
    if (p % q) {
      cout << p << endl;
      continue;
    }
    vector<long long> num;
    long long ans = p;
    for (long long i = 1; i <= sqrt(q); i++) {
      if (q % i == 0) {
        num.push_back(i);
        num.push_back(q / i);
      }
    }
    for (long long i = 0; i < num.size(); i++) {
      if (num[i] == 1) continue;
      long long pp = p;
      long long cnt = 0;
      while (pp % num[i] == 0) {
        if (pp % q) break;
        pp /= num[i];
        cnt++;
      }
      long long tmp = pow(num[i], cnt);
      ans = min(ans, tmp);
    }
    cout << p / ans << endl;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  solve();
  return 0;
}
