#include <bits/stdc++.h>
using namespace std;
long long bPow(long long a, long long n) {
  if (n == 0) return 1;
  long long p = bPow(a, n / 2);
  p *= p;
  if (n % 2) p *= a;
  return p;
}
signed main() {
  long long t;
  cin >> t;
  for (long long i = 0; i < t; i++) {
    long long p, q;
    cin >> p >> q;
    map<long long, long long> qDivs;
    map<long long, long long> pDivs;
    long long q1 = q;
    long long temp = 2;
    while (q1 != 1) {
      if (temp * temp > q1) {
        qDivs[q1]++;
        break;
      }
      if (q1 % temp) {
        temp++;
        continue;
      }
      q1 /= temp;
      qDivs[temp]++;
    }
    long long p1 = p;
    for (auto& it : qDivs) {
      while (p1 % it.first == 0) {
        p1 /= it.first;
        pDivs[it.first]++;
      }
    }
    if (p1 != 1) {
      pDivs[p1]++;
    }
    long long mx = 0;
    if (p % q) {
      mx = p;
    }
    for (auto& it : qDivs) {
      if (!pDivs[it.first]) continue;
      long long minM = it.second - 1;
      if (it.second == 0) minM = 0;
      long long x = p / bPow(it.first, pDivs[it.first] - minM);
      if (p % x == 0 && x % q) {
        mx = max(mx, x);
      }
    }
    cout << mx << endl;
  }
}
