#include<iostream>
using namespace std;
int main(){
    int T;
    cin>>T;
    while(T--){
        long long n;
        cin>>n;
        int cnt2=0,cnt3=0,cnt5=0;
        while(n%2==0){
            cnt2++;
            n/=2;
        }
        while(n%3==0){
            cnt3++;
            n/=3;
        }
        while(n%5==0){
            cnt5++;
            n/=5;
        }
        if(n!=1){
            cout<<-1<<endl;
            continue;
        }
        int steps=0;
        steps+=cnt5;
        cnt2+=2*cnt5;
        steps+=cnt3;
        cnt2+=cnt3;
        steps+=cnt2;
        cout<<steps<<endl;
    }
    return 0;
}