MathNet 1988 — Part 01 Question 2

Let $N$ be the natural numbers and $N' = N \setminus \{0\}$. Find all functions $f: N' \to N$ such that $f(xy) = f(x) + f(y)$, $f(30) = 0$ and $f(x) = 0$ for all $x \equiv 7 \pmod{10}$.