Onmatu- Pre-Algebra Article

How to recognize that the number is divisible by 2 and 3


We will learn together how to recognize that the given number is divisible by 2 and 3. First we show a rule for recognizing that the number is divisible by 2. The rule is simple: if the last digit of the given number is divisible by 2 then the number is divisible by 2.

We start with examples of two digit numbers. They are: 12, 26, 34, 46, 88, 96 and so on. We see that the last digits of these numbers are 2, 6, 4, 8 and 6 and they are divisible by 2.

Can you give your own examples of two digit numbers that are divisible by 2?

Now we give examples of three digit numbers that are divisible by 2. They are: 332, 100, 438, 376, 552, 500 and so on. Remember that when the last digit of a number is 0, the number is divisible by 2 as we count 0 as 10 (like in the case of subtraction of 100 and 3, for example).

If we go to  four digit numbers, here are some examples: 4000, 3002, 5752, 6798, 8876, 9354 and so on.

Now your turn. Can you give examples of five digit numbers that are divisible by 2?

Let's see now a rule for recognizing that the number is divisible by 3.  The rule is easy to remember and it states the following. When we add up digits of the given number and get a number that is divisible by three, then our number is divisible by 3. We learn best from examples and here we go. :)
Let's start from two digit numbers. Number 57 is divisible by 3 because

5 + 7 = 12,

1 + 2 = 3.

An example of three digit number divisible by 3 is 588, because  

5 + 8 + 8 = 21,

2 + 1 = 3.


In the end we give an example of four digit number that is divisible by 3. Number 5670 is divisible by 3, because

5 + 6 + 7 + 0 = 18,

1 + 8 = 9.

One task for you. Tell what number is divisible by 2, by 3 and which number is not divisible by 2 nor by 3. Numbers are:

26759, 657, 53382, 78990, 62625, 7564, 889292, 454, 7669087654.

Can one number be divisible by 2 and by 3 at the same time?

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