These is the divisibility rule by 4, 25, 100?

Question

I need to find the divisibility rule by 4, 25 and 100. I want to know if my answer it is correct!

Knowing that: \begin{align} 100\equiv0\mod4, \mod 25 , \mod100 \to \\ 10^2 \equiv 0 \mod 4 , \mod25, \mod100 \end{align}

So, for n $\ge 2$, we have: \begin{align} a_210^2 \equiv 0 \mod4, \mod25, \mod100 \to\\ a_n10^n \equiv0 \mod4, \mod25, \mod100 \end{align}

For $a =a_na_{n-1}...a_2a_1a_0$ in base 10, we have that $a \equiv 10a_1+a_0 \mod4, \mod25, \mod100 $, for to be divisibily for 4, 25, 100. In other words, $a_1a_0 = 0.$