Divisibility by 2

How do we know if a number is divisible by a certain number?

In this post, the first post in the Divisibility Rules Series, we examine why a number is divisible by 2 if it is even.  In this post, since we are talking about divisibility rules, when we use the word number, we mean integer.

Since multiplication and division are inverses of each other, we can examine what happens if a number is multiplied by 2. Let’s try a few examples:

0 x 2 = 0
1 x 2 = 2
2 x 2 = 4
3 x 2 = 6
4 x 2 = 8
5 x 2 = 10
6 x 2 = 12
7 x 2 = 14
8 x 2 = 16
9 x 2 = 18

From the list above, we make the following observations: (1) the ones digit of numbers  multiplied by 2 is either 0, 2, 4, 6, or 8; and (2) if the numbers are consecutive the pattern repeats.

Since we have exhausted all 1-digit numbers in the list above, it is clear that the ones digit of a number multiplied by 2 cannot be 1, 3, 5, 7 or 9.  Therefore, we can conclude that a number is divisible 2 if its ones digit is even.

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