CR-MO 2016 F3

Let $f: Z^+ \to Z^+ \cup \{0\}$ a function that meets the following conditions: a) $f (a b) = f (a) + f (b)$ , b) $f (a) = 0$ provided that the digits of the unit of $a$ are $7$ , c) $f (10) = 0$ . Find $f (2016).$