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2.5

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds MICHAEL 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 17 seconds MICHAEL ANDERSON: So I know that’s in the 3 times table.

Skip to 0 minutes and 19 seconds PAULA 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 seconds MICHAEL ANDERSON: OK. So what if we had the number 123?

Skip to 0 minutes and 40 seconds PAULA 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 52 seconds PAULA KELLY: 6 is a multiple of 3. We know our original number, 123, is also a multiple of 3.

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

Skip to 1 minute and 6 seconds PAULA 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 16 seconds PAULA KELLY: So 124 is not a multiple of 3.

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

Skip to 1 minute and 25 seconds PAULA 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 38 seconds PAULA 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 seconds MICHAEL 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.

# 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