Lesson video

- Hi everyone.

I'm Mr. Lund and in this video, we're going to be looking at finding the highest common factor using Venn diagrams. Hi everyone.

We can use prime factors with Venn diagrams to work out the highest common factor of two numbers.

Here is the number 80 and the number 30 broken down into its prime factors.

Here's a Venn diagram.

Let's start our process by using our factor trees to see which primes are common between both our numbers.

If they are common, we place them in the intersection of the Venn diagram.

Don't forget to cross them off your factor trees then complete your Venn diagram.

Remember to cross off your primes from your factor tree and there we go.

We can use this information to help us find the highest common factor and the highest common factor is the product of the numbers inside the intersection.

In this example, the numbers five and two multiplied together, give you an answer of 10.

Therefore the highest common factor of 80 and 30 is 10.

Now you might say, "Oh, I could have figured that out "without all this kerfuffle." And yes you could, but as numbers get much larger, this technique helps to organise your working.

Here's an example for you to try, pause the video and return to check your answers.

Here's the solution for question number one.

Now we could create a factor tree with the number 40 that looked like this.

There we go.

The product of prime factors is unique to every number that it represents.

Here's the next question, a lovely number two.

Pause the video and return to check your answers.

Here's the solutions to question number two.

Some of you are thinking, "Why do I need to go "through this really complex matter "to find the highest common factor "when I can work it out quite simply in my head?" The point is you may be asked to do something like this in your exam, but also as numbers get larger, this is a useful technique if you don't have a calculator or a computer.

If you can work out these answers without using a Venn diagram, that's absolutely fine.

Pause the video and return to check your answers.

Here's the solutions to question number three.

Make sure you're orderly and organised in your working out.

If you didn't use Venn diagrams, that's fine.

For catching this far, here's the question four.

Pause video and return to check your answers.

Here's the solution question number four.

Did you notice in the intersection of the Venn diagram, there were no numbers whatsoever.

That means that the highest possible common factor is simply one.