codeforces 1445C（质因数分解）

#include<bits/stdc++.h>
#define x first
#define y second
#define PB push_back
#define mst(x,a) memset(x,a,sizeof(x))
#define all(a) begin(a),end(a)
#define rep(x,l,u) for(ll x=l;x<u;x++)
#define rrep(x,l,u) for(ll x=l;x>=u;x--)
#define sz(x) x.size()
#define IOS ios::sync_with_stdio(false);cin.tie(0);
using namespace std;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<char,char> PCC;
typedef long long ll;
typedef pair<ll,ll> PLL;
const int N=1e5+10;
const int M=1e6+10;
const int INF=0x3f3f3f3f;
const int mod=1e9+7;
void solve(){
    ll p,q;cin>>p>>q;
    if(p%q!=0) {cout<<p<<endl;return;}
    ll x=q;
    ll ans=1;
    rep(i,2,x/i+1){
        if(x%i==0){
            while(x%i==0) x/=i;
            ll ss=p;
            while(ss%q==0) ss/=i;
            ans=max(ans,ss);
        }
    }
    if(x>1){
        ll ss=p;
        while(ss%q==0) ss/=x;
        ans=max(ans,ss);
    }
    cout<<ans<<endl;
}
int main(){
    IOS;
    //freopen("test.txt", "r", stdin);
    //freopen("test.txt", "w", stdout);
    int t;cin>>t;
    while(t--)
        solve();
    return 0;
}