Q$3$ Recognizing decimal integers multiples of $3$

$1$ Point

Grading comment:

Let string s in $\{0,...,9\}*.$Let n be a string s interpreted as a decimal integer $.$Draw a DFA that accepts s if and only if n is a multiple of $3$ i$.$e$.,3,6,9,12,15,...$ etc. Assume $($the empty string$)$ is not accepted.

Remember:

s is consumed by the DFA as a string. So if e$.$g$.,$ s$=123,$ then $1$ is input into the machine, followed by $2,$ followed by $3.$

However, when interpreted as an integer, n$=123=3\mathrm{.}41,$ which is a multiple of $3.$ Therefore the string s$=123$ should be accepted.