## Divisibility by 6

This is the fifth post in the Divisibility Rules Series.  In the previous posts, we have discussed divisibility by 2, 3, 4, 5 and 10. In this post, we discuss divisibility by 6.

First, we observe that all multiples of six (6, 12, 18, 24 …) are even. We are sure of this because any number multiplied by an even number is even.  Also, we can observe that  multiples of 6 are also divisible by 3: 6(1), 6(2), 6(3), 6(4) =   (2)(3)(1), (2)(3)(2), (2)(3)(3), (2)(3)(4),…. This, of course, follow from the fact that 6 is divisible by 3. Therefore, a number is divisible by 6 if it is divisible by 2 and it is divisible by 3.

In general, all multiples of 6 are in the form 6k, where k is any integer. But 6 is both divisible by 2 and 3. Therefore, a number is divisible by 6 if it is divisible by 2 and 3.

## Divisibility by 3

This is post is the fourth part of the Divisibility Rules Series.  The first three posts are about divisibility by 2, divisibility by 4 and divisibility by 5 and 10. In this post, we discuss divisibility by 3.

When we divide things, we split them into ‘groups.’ Of course, we cannot always divide them equally.  For example, dividing 13 balls by 3 is the same as putting the balls into containers in groups of three. In dividing 13 by 3, 1 is left out as shown below. We have learned that the excess or the ones that are left out during division are called remainders. In the figure below, we can say that 13 divided by 3 gives a remainder of 1.

Divisibility by 3 is not as easy as divisibility by 2, by 5 or by 10. However, we note the following observations when we divide by 3. » Read more

## Divisibility by 5 and 10

This is the third post in the Divisibility Rules Series.  The first was about divisibility by 2 and the second was about divisibility by 4.  In this post, we discuss divisibility by 5 and 10.

If we skip count by 10, we will immediately realize that the numbers always end in zero: 10, 20, 30, 40, and so on. It is clear that all multiples of 10 end in 0; therefore,  a number is divisible by 10 if the ones digit is 0.

On the other hand, if we skip count by 5, then we have 5, 10, 15, 20, 25, 30 and so on. Notice that if we add 5 to a number whose ones digit is 5, the ones digit of the sum is 0. Similarly, any number whose ones digit is 0 added to 5, the ones digit of the sum is always 5.  Hence, we conclude that a number is divisible by 5, if the ones digit is either 5 or 0.

From here, we can see clearly that all numbers that are divisible by 10 are also divisible by 5.

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