finite automata that accepts integers divided by 3?
I believe you are misunderstanding the way finite automata work. A finite automaton accepts a language, i.e. a subset of the finite strings of a given finite alphabet. In your case, the accepted language is the set of strings made of $0$ and $1$ which encode a well-formed multiple of $3$.

Given a string, imagine placing a token on the initial state, then for each character of the string, left to right, move the token along the transition labelled $0$ or $1$, according to which character you read.

After having consumed each character of the string, the automaton accepts if and only if the token is on one of the accepting states.

Considering your automaton, intuitively, the top three states determine whether the string encodes a well-formed number (i.e. a string that starts with $1$ or is exactly $0$, for instance, $1000$ is valid, but $000$ isn't) while the bottom three determine whether or not it is divisible by $3$ using elementary number theory.