Let decimal representation of \(n\) be \[n = d_k d_{k-1} \dots d_2 d_1\] Expand the number to separate the last \(2\) digits. \[d_k d_{k-1} \dots d_3 \cdot 100 + d_2 d_1\] \[= 4 \cdot k + d_2 d_1\] where \(k\) represents the integer \(d_k d_k-1 \dots d_3 \cdot 25.\)

If \(d_2 d_1\) is a multiple of \(4\) then \(d_2 d_1 = 4 \cdot j\) for some integer \(j,\) in which case \(n = 4 \cdot (k + j)\) and is divisible by \(4.\) On the other hand, if \(d_2 d_1\) is not divisible by \(4\) then \(d_2 d_1 = 4 \cdot j + r\) for some integers \(j\) and \(1 \leq r \leq 3.\) In this case, \(n = 4 \cdot (k + j) + r\) and is not divisible by \(4.\)