#include <bits/stdc++.h>
using namespace std;
int n, m, k, z, f[100039], s[100039], d[100039], head, dh, t, sh;
map<long long, int> q;
long long x, y, now, tot, pus, ans, flag;
int main() {
  register int i, j;
  for (i = 2; i * i <= 1e9; i++) {
    if (!f[i]) s[++head] = i;
    for (j = 1; j <= head && i * s[j] <= 100000; j++) {
      f[i * s[j]] = 1;
      if (i % s[j] == 0) break;
    }
  }
  scanf("%d", &t);
  while (t--) {
    scanf("%lld%lld", &x, &y);
    now = y;
    dh = sh = 0;
    pus = 1e18;
    for (i = 1; s[i] * s[i] <= y && i <= head; i++) {
      if (now % s[i] == 0) {
        d[++dh] = s[i];
        while (now % s[i] == 0) q[s[i]]++, now /= s[i], sh++;
      }
    }
    if (now != 1) q[now]++, d[++dh] = now, sh++;
    now = x;
    for (i = 1; i <= dh; i++) {
      if (x % d[i] == 0) {
        ans = 0;
        while (x % d[i] == 0) x /= d[i], ans++;
        if (ans >= q[d[i]]) {
          tot = 1;
          for (j = 1; j <= ans - q[d[i]] + 1; j++) tot *= d[i];
          pus = ((pus) < (tot) ? (pus) : (tot));
        }
        sh -= ((q[d[i]]) < (ans) ? (q[d[i]]) : (ans));
      }
    }
    if (sh)
      printf("%lld\n", now);
    else
      printf("%lld\n", now / pus);
    q.clear();
  }
}
