Divisibility by 8

This is the seventh post in the Divisibility Rules Series.  In this post, we will discuss divisibility  by 8.

A number is divisible by 8 if the last three digits is divisible by 8. For example, 25816 is divisible by 8 since 816 is divisible by 8. On the other hand, 5780 is not divisible by 8 since 780 is not divisible by 8. Why is this so?

Let us start with 25 816. First, we know that 1000 is divisible by 8. Therefore, 2000, 3000, 4000, and all multiples of 1000 are divisible by 8. Since 25 816 = 25000 + 816 and 25 000 is divisible by 8, we just have examine the last three digits. Notice that this is similar to 5780. Since 5780 = 5000 + 780, and 5000 is divisible by 8, we are sure that it is not divisible by 8 since the last three digits is not divisible by 8.

This observation can be generalized because all numbers greater than 1000 can be expressed as multiple of 1000 + three-digit number (the hundreds, tens, and ones). Since all multiples of 1000 are divisible by 8, we just have to examine the divisibility of the last three digit number.

divisibility by 8

Of course this observation is also similar with negative numbers. All negative numbers less than -1000 can can be expressed as multiple of -1000 + three-digit negative number.

Related Posts Plugin for WordPress, Blogger...

2 thoughts on “Divisibility by 8

Leave a Reply