Question

All numbers which are divisible by 4 must also be divisible by 8.

Answer 1

Let the number divisible by 4 be 4k, where k is any positive integer.

We know that k can be of the form 2m or 2m+2.

Case 1:

4(2m) = 8m

8m is divisible by 8.

Case 2:

4(2m+2) = 8m+8 = 8(m+1) = 8a, where a = m+1.

8a is divisible by 8.

Therefore, all numbers which are divisible by 4 are divisible by 8, except the number 4.