#include <bits/stdc++.h>
using namespace std;
long long t = 1, n, a, b, c[1000009], d[1000009];
map<long long, long long> mp2;
long long qp(long long x, long long y) {
  if (!y) return 1;
  long long p = qp(x, y / 2);
  if (y & 1) return p * p * x;
  return p * p;
}
int main() {
  cin >> t;
  while (t--) {
    long long c1 = 0, c2 = 0, ans, aa = 1e18, f = 0;
    cin >> a >> b, ans = a;
    for (long long i = 2; i <= sqrt(b); i += 1)
      if (!(b % i)) d[c2++] = i, mp2[i] += 1, b /= i, i -= 1;
    if (b > 1) d[c2++] = b, mp2[b] += 1;
    for (long long i = 0; i < c2; i += 1) {
      if (i && d[i] == d[i - 1]) continue;
      if (a % d[i]) {
        f = 1;
        break;
      }
      long long aaa = a, cur = 0;
      while (!(aaa % d[i])) aaa /= d[i], cur += 1;
      if (cur >= mp2[d[i]]) aa = min(aa, qp(d[i], cur - mp2[d[i]] + 1));
    }
    for (long long i = 0; i < c2; i += 1)
      if (a % d[i]) f = 1;
    for (long long i = 0; i < c2; i += 1) mp2[d[i]] = 0;
    if (f == 1)
      cout << ans << endl;
    else
      cout << (aa < 1e18 ? ans / aa : ans) << endl;
  }
  return 0;
}
