#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int tc;
ll a, b, INF = 1e9;
int main() {
  scanf("%d", &tc);
  while (tc--) {
    scanf("%lld %lld", &a, &b);
    if (a % b) {
      printf("%lld\n", a);
      continue;
    }
    ll A = a, B = b;
    ll mx = 0;
    for (ll i = 2; i * i <= INF; i++) {
      if (i == 1) break;
      if (b % i == 0) {
        int c1 = 0, c2 = 0;
        while (b % i == 0) b /= i, c1++;
        while (a % i == 0) a /= i, c2++;
        int c = c2 - (c1 - 1);
        ll g = 1;
        for (int j = 1; j <= c; j++) g *= i;
        mx = max(mx, A / g);
      }
    }
    if (b > 1) {
      int c1 = 1, c2 = 0;
      while (a % b == 0) a /= b, c2++;
      int c = c2 - (c1 - 1);
      ll g = 1;
      for (int j = 1; j <= c; j++) g *= b;
      mx = max(mx, A / g);
    }
    printf("%lld\n", mx);
  }
}
