#include <bits/stdc++.h>
using namespace std;
int main() {
  int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    long long int cnt = 0, flag = 0;
    while (n > 1) {
      if (n % 2 == 0) {
        n = n / 2;
        cnt++;
      } else if (n % 3 == 0) {
        n = (2 * n) / 3;
        cnt++;
      } else if (n % 5 == 0) {
        n = (4 * n) / 5;
        cnt++;
      } else {
        flag = 1;
        break;
      }
    }
    if (flag == 1) {
      cout << -1;
    } else {
      cout << cnt;
    }
    cout << endl;
  }
  return 0;
}
