How do you prove that the set of decimal representation of the 4 divisble natural numbers is regular? This is from an old exam, the last Task no one could solve correctly and I'm curious how it's done :p

Show that the set of decimal representation (without leading zeroes) of the divisible numbers by 4 (natural numbers) is regular.

By this thread How to prove a language is regular? I know that one can make a DFA to Show that a language is regular.

But is that possible at all because we have infinite natural numbers that are divisible by 4..

I cannot even imagine how that DFA would look like :o

Maybe there is another way of showing this, too?

Edit: Removed..
A decimal number is divisible by 4 if the number formed by its last two digits are divisible by 4. Stated differently, divisibility by 4 depends only on the last two digits. That should be enough for you to show that your language is regular.

The language of numbers in base $b$ divisible by $m$ is regular for all $b,m$, but that's somewhat harder to show.