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