Skip to 0 minutes and 7 secondsMICHAEL ANDERSON: So there's a really nice method to tell whether a number is divisible by 3 or not. Shall we have a look?

Skip to 0 minutes and 13 secondsPAULA KELLY: OK. If we start with the number 36, for example-- OK?

Skip to 0 minutes and 17 secondsMICHAEL ANDERSON: So I know that's in the 3 times table.

Skip to 0 minutes and 19 secondsPAULA KELLY: And let's just show you how that works. So if you have the number 36, our test is, if we add our digits together-- so if we did 3 plus 6, that would give us 9. As 9 is a multiple of 3, we know that our whole number is also a multiple of 3.

Skip to 0 minutes and 36 secondsMICHAEL ANDERSON: OK. So what if we had the number 123?

Skip to 0 minutes and 40 secondsPAULA KELLY: OK. So 123. We're going to add our digits, so 1 plus 2 plus 3. That's going to give us 6 altogether.

Skip to 0 minutes and 51 secondsMICHAEL ANDERSON: Yeah.

Skip to 0 minutes and 52 secondsPAULA KELLY: 6 is a multiple of 3. We know our original number, 123, is also a multiple of 3.

Skip to 0 minutes and 59 secondsMICHAEL ANDERSON: So 124?

Skip to 1 minute and 2 secondsPAULA KELLY: So we know this shouldn't work, because that's just 1 more.

Skip to 1 minute and 5 secondsMICHAEL ANDERSON: Uh-huh.

Skip to 1 minute and 6 secondsPAULA KELLY: So we had 1 plus 2 plus 4. If we add our digits, we get 7. It's not a multiple of 3.

Skip to 1 minute and 15 secondsMICHAEL ANDERSON: Right. OK.

Skip to 1 minute and 16 secondsPAULA KELLY: So 124 is not a multiple of 3.

Skip to 1 minute and 19 secondsMICHAEL ANDERSON: OK. So what about something a bit larger, like 357?

Skip to 1 minute and 25 secondsPAULA KELLY: OK. So if we try 357, same again. We have 3 plus 5 plus 7. If we add our digits together, we get 15.

Skip to 1 minute and 37 secondsMICHAEL ANDERSON: OK.

Skip to 1 minute and 38 secondsPAULA KELLY: OK? Now, we know that is a multiple of 3, but just to show it really does work-- and you may get some larger numbers than 15-- we'll have our same method. So 15, if we do our digits added together, are 1 plus 5. We're going to have 6. That is a multiple of 3, so 357 is also a multiple of 3.

Skip to 2 minutes and 0 secondsMICHAEL ANDERSON: So you can keep repeating the process until you come to a single-digit number. And if that number is 3, 6, or 9, then your original number will be in the 3 times table.

Skip to 2 minutes and 9 secondsPAULA KELLY: Exactly.

Divisibility rules: multiples of 3

We saw in the last video that the digit in the units column will indicate whether a numbers is a multiple of 2, 5 or 10, but the same method cannot be used to determine whether a number is divisible by 3.

Consider the number 438 again. Do you think this number is exactly divisible by three and therefore in the three times table? You might divide 438 by 3 using a calculator to see whether you get a whole number, but what if a calculator is not permitted? One approach would be to count up in threes to see whether 438 is in the 3 times table, but this method is not very efficient.

In this video, Paula and Michael explain a simple test to determine whether a number is divisible by 3. When you have watched the video, use the method to determine whether 438 is exactly divisible by 3.

Problem worksheet

Now complete question 3 from this week’s worksheet

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This video is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre