We have:

\(\overline{a_na_{n-1}...a_3a_2a_1}=\overline{a_na_{n-1}..a_4}.1000+\overline{a_3a_2a_1}\)

Since \(1000⋮4\) => \(\overline{a_na_{n-1}..a_4}.1000\) \(⋮\) \(4\).

\(\overline{a_na_{n-1}...a_3a_2a_1}\)  \(⋮\) \(4\)  iff   \(\overline{a_3a_2a_1}\) \(⋮\)  \(4\)

In other word: a number is divisibility by 4 if only if the number formed by its three right digits is divisibility by 4.

Another way:

We have: ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯xnxn−1...x3x2x1=100.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯xnxn−1...x3+¯¯¯¯¯¯¯¯¯¯¯x2x1

Since 100⋮4

=>100.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯xnxn−1...x3⋮4

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯xnxn−1...x3x2x1⋮4

=>¯¯¯¯¯¯¯¯¯¯¯x2x1⋮4

In other word: a number is divisibility by 4 when the last three digits on the right-hand is divisibility by 4

Another way:

We have: \(\overline{x_nx_{n-1}...x_3x_2x_1}=100.\overline{x_nx_{n-1}...x_3}+\overline{x_2x_1}\)

Since \(100⋮4\)=>\(100.\overline{x_nx_{n-1}...x_3}⋮4\)

\(\overline{x_nx_{n-1}...x_3x_2x_1}⋮4\)=>\(\overline{x_2x_1}⋮4\)

In other word: a number is divisibility by 4 when the last three digits on the right-hand is divisibility by 4