3 Times is a charm

3 divisibility rule

If a number  is divisible by 3, then the sum of the digits of the number are also divisible by 3.

As an example:

63, 123, 2223 are all divisible by 3.  We can easily determine this in our heads without a calculator by adding the digits and then dividing by 3 as follows:

6+3=9 

9÷3=3

63 is evenly divisible by 3.

If we use a calculator, we find 63÷3=21

1+2+3=6

6÷3=2

123 is divisible by 3.

If we use our a calculator, we find 123÷3=41

2+2+2+3=9

9÷3=3

2223 is divisible by 3
If we use our calculator, we find 2223÷3=741

89, 173, and 3113 are not divisible by 3.  Here is why:

8+9=17 and 17 is not divisible by 3

1+7+3=11 and 11 is not divisible by 3

3+1+1+3=8 and 8 is not divisible by 3

This is a very simple rule yet very powerful.  There are other rules that I will present a little later but this is one of the most important rules and this will help you through many tests like the SAT and ACT.

Try these on your own:

Are these numbers divisible by 3?  Add the digits and divide.  Check with your calculator.

1234, 174, 12761, 25437

Hint all are except 12761.