Since 100 divided by 4 has a remainder of 0, we can write 100 ≡ 0 (mod 4). Therefore 10k ≡ 0 (mod 4) for k=2,3,4…. Then,
x≡ a0 + a1 (10) + a2 (0) + a3 (0)+…+am (0) (mod 4)
≡ a0 + a1 (10) (mod 4).
Therefore x is divisible by 4 if and only if the number a0 + a1 (10) is divisible by 4 where a0 + a1(10) is the number formed by the last two digits of the number x.