I think this solution is not correct.
It does not (properly) check whether the elements of sys are coprime.
Instead it just checks if sys contains more than one even number - which is just a special case.

The solution would for example fail to return "Not applicable" for [3, 6].

I like this iterative solution.
Recursion might be the "right" way to do factorial() in a functional language, but in Java it's just slower.