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Dividing by 3

Is 2000 a multiple of 3?

You could use your calculator and work out 2000/3 and see if the answer is a whole number or not.

There is an even quicker way in this case - and you don't even need a calculator!
To see if a number is exactly divisible by 3 just add up all its digits. If that sum is divisible by 3, then so is the original number. For example:
is 2000 a multiple of 3?
adding the digits is easy! 2+0+0+0 = 2
and since 2 is not a multiple of 3, then 2000 is not a multiple of 3 either.
What about 111111111?

Is it exactly divisible by 3?

Using the add-the-digits test, 1+1+1+1+1+1+1+1+1 is 9, and 9 is a multiple of 3 so therefore 111111111 is exactly divisible by 3.

Quick tip 1

We are only interested in the digit-sum being a multiple of 3 or not. So we can apply the same trick to the digit sum itself to see if it also is or isn't a multiple of 3 and we can keep doing this until we get a single digit-sum!
For instance, 9675 has a digit sum of 9+6+7+5=27 and 2+7 is 9. Since 9 is a multiple of 3 then so is 9675.

Quick tip 2

0's, 3's, 6's and 9's in the number can safely be ignored when finding the digit sum as they are multiples of 3.
So, for instance, with the same example as in Quick Tip 1, 9675, we can forget the 9 and the 6 when adding the digits. 7+5=12 and, using Quick Tip 1, 1+2=3, so, again, we find 9675 is a multiple of 3.

You can practice these rules using this interactive panel:

Practice Panel for Divisibility by 3

a multiple of 3.

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Primes, Factors and Divisibility