This is the seventh post in the Divisibility Rules Series. In this post, we will discuss divisibility by 8.
A number is divisible by if the last three digits is divisible by . For example, is divisible by since is divisible by 8. On the other hand, is not divisible by since is not divisible by . Why is this so?
Let us start with . First, we know that is divisible by . Therefore, , , , and all multiples of are divisible by . Since and is divisible by , we just have examine the last three digits. Notice that this is similar to . Since , and is divisible by , we are sure that it is not divisible by since the last three digits is not divisible by .
This observation can be generalized because all numbers greater than can be expressed as multiple of 1000 + three-digit number (the hundreds, tens, and ones). Since all multiples of are divisible by , we just have to examine the divisibility of the last three digit number.
Of course this observation is also similar with negative numbers. All negative numbers less than can can be expressed as multiple of -1000 + three-digit negative number.