Want to keep learning?

This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Understanding Numbers. Join the course to learn more.

Skip to 0 minutes and 7 seconds PAULA KELLY: So let’s have a look at some divisibility tests. So if we look at nine numbers, I know that any number that ends in a 0 can be divided by 10.

Skip to 0 minutes and 17 seconds MICHAEL ANDERSON: Yeah. So it might be a good test to see whether a number is a multiple of another number by looking at the digits in the units column– so what the number ends in.

Skip to 0 minutes and 27 seconds PAULA KELLY: OK.

Skip to 0 minutes and 28 seconds MICHAEL ANDERSON: So if a number ends in a 0, like you were saying, it’s definitely in the 10 times table. Similarly, if it’s in the 5 times table– well, the 5 times table goes 5, 10, 15, 20. So if it ends in a 0 or a 5, we know it’s going to be a multiple of 5.

Skip to 0 minutes and 45 seconds PAULA KELLY: OK. Similarly, with our multiples of 2, we would have 0, 2, 4, 6, 8, 10, 12, 14. So our pattern is repeating.

Skip to 0 minutes and 56 seconds MICHAEL ANDERSON: So yeah. So if a number ends in 0, 2, 4, 6, or 8– so if it ends in an even number– then it’s going to be a multiple of 2.

Skip to 1 minute and 5 seconds PAULA KELLY: OK. That’s our 2s. What about our 3s?

Skip to 1 minute and 8 seconds MICHAEL ANDERSON: So let’s have a look at the 3 times table. We start with 3, and then we go to 6. 6 goes to 9. 9 goes to 2.

Skip to 1 minute and 19 seconds PAULA KELLY: Because we have 12. Yes.

Skip to 1 minute and 21 seconds SPEAKER 2: Then 15 ends in 5. 18 ends in 8. Then we go to 21, 24, 27, and then 30, and then 33, and the pattern seems to repeat. Now, unfortunately, we’ve called in every single number. So in the 3 times table, we’ll have every single digit in the units column. So by looking at the last digit, that’s not really helped us.

Skip to 1 minute and 51 seconds PAULA KELLY: OK, so using this method, we can’t see a general pattern whether numbers can be divided by 3.

Skip to 1 minute and 58 seconds MICHAEL ANDERSON: No, unfortunately not. It’s a really nice pattern, but it doesn’t really help us to tell whether a number is divisible by 3 or not. So let’s take a look at a divisibility test for the 3s.

Divisibility rules: looking at units

In this and the next step, we’ll be looking at divisibility rules. Here we use properties of numbers to work out whether they are divisible by other numbers without a remainder. Think of a large number say 438. Without using a calculator, how would you know whether this number would divide exactly by 2 without leaving a remainder?

In this video, Michael and Paula explain how consideration of just the units digit, could help us determine whether a number is divisible by another number. For example, 438, we would just look at the digit 8 to determine whether 438 was divisible exactly by 2.

These are interesting properties of numbers, but all they tell you is if the number is divisible by another number without the remainder, not the result of any calculation. Tests for divisibility are used in error checking. Computer codes with check digits are widely used in the retail and banking sector.

Teaching resources

  • One long-established code, the International Standard Book Number (ISBN), uses check digits and rules for divisibility to ensure ISBN numbers are valid. This teaching resource explores ISBN numbers further.
  • Credit card errors resource explains the check digit algorithm invented by Hans Luhn. This algorithm is widely used for both credit and debit cards to check small errors in the input of card numbers, using the final digit on the card as a check.

Share this video:

This video is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre