(Hard) FSM to Check Divisibility

Howdy everyone!

I know it’s been a while since the last question of the day…been busy with my day job. My apologies.

So here is something a little different which I came across the other day:

Can you describe a full FSM which can check if a binary number is divisible by 3? Be sure to describe in what manner the data is coming into our FSM and any limitations as well.

Good Luck!