# Lexical Number Theory

**Computer Science**Level 4

Assume that the strings accepted by the automata below are interpreted as binary numbers.

What is the largest integer \(n\) such that the set of integers accepted by the automata are always divisible by \(n\)?

**Extra Credit:** Prove your answer.

**Extra Extra Credit:** Is it always possible to form such an automata, for any \(n\)? If not, why not? If yes, how?