# Number Theory with Finite State Machines

Assume that the strings accept 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 be divisible by $$n$$?

Clarification: Empty string is considered as equivalent to 0 in this question.

Extra Credit: Both this FSM and the one in Agnishom Chattopadhyay's question (linked below) has three states. But the answers are different. Account for this phenomenon.

Inspiration: Lexical Number Theory

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