This question should be solved with pigeonhole principle.
Let $a,n \in \mathbb N$ such that $a$ is a number whose digits are only $3$'s and $0$'s, and $n$ is an unspecified natural number.
Show that there is some number $a$ such that $a$ is divisible by $n$.
Hint: the pigeonholes are the $n$ possible remainders upon division by $n$. Now you just need to choose appropriate pigeons, and demonstrate that a collision will get you the desired property.