Divisibility Rules of Whole Numbers Made Simple

by Paul Chika Emekwulu

In a mental arithmetic, a group of students were asked whether 486,459 was divisible by 3. They were asked to answer yes or no but be ready to explain their answers. In a private session with the teacher, one of the students, Akeem, was asked why he did not have any answer to the above question. His reply was that 486,459 was too big a number to be divisible by 3.
On the other hand, another student named Doug answered yes to the same question and went further to explain that the sum of the digits in 486,459 is equal to 36
(i.e. 4 + 8 + 6 + 4 + 5 + 9),

and since 36 is divisible by 3, then 486,459 is also divisible by 3.

Doug was right.

Doug’s reasoning is based on the divisibility rule by 3.

The numbers 2, 3, 4, 5, 6, 7 8, 9, 10, and 11 have their own individual divisibility rules.

These rules are collectively called rules of divisibility.

In the following chapters on divisibility rules, we shall introduce each of them, and take it to the next level by using algebra (in some cases, in addition to arithmetic) to investigate why the divisibility rule works. The investigations are interesting, and you will enjoy them when you eventually discover that just memorizing these divisibility rules is not enough

119 pages, Kindle Edition

First published May 23, 2015