#include <bits/stdc++.h>
using namespace std;
long long int power(long long int n, long long int m) {
  if (m == 0) return 1;
  long long int ans = power(n, m / 2);
  ans = ans * ans;
  if (m % 2 == 1) ans = ans * n;
  return ans;
}
signed main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
  long long int T = 1;
  cin >> T;
  bool p[31624];
  for (long long int i = 2; i <= 31623; ++i) {
    p[i] = 1;
  }
  for (long long int i = 2; i * i <= 31624; ++i) {
    if (p[i]) {
      for (long long int j = i * i; j <= 31623; j += i) {
        p[j] = 0;
      }
    }
  }
  vector<long long int> pr;
  for (long long int i = 2; i <= 31623; ++i) {
    if (p[i]) pr.push_back(i);
  }
  while (T--) {
    long long int a, b;
    cin >> a >> b;
    if (a < b) {
      cout << a << "\n";
      continue;
    }
    if (a % b != 0) {
      cout << a << "\n";
      continue;
    }
    map<long long int, long long int> m1, m2;
    long long int ans = 1e18;
    for (long long int x : pr) {
      while (b % x == 0) {
        m1[x]++;
        b /= x;
      }
    }
    if (b != 1) m1[b]++;
    long long int a1 = a;
    for (auto x : m1) {
      while (a1 % (x.first) == 0) {
        m2[x.first]++;
        a1 /= (x.first);
      }
      ans = min(ans, power(x.first, m2[x.first] - x.second + 1));
    }
    if (b != 1) {
      while (a1 % b == 0) {
        m2[b]++;
        a1 /= b;
      }
      ans = min(ans, power(b, m2[b]));
    }
    cout << a / ans << "\n";
  }
  return 0;
}
