Lesson video

Hi there and welcome to another maths lesson with me Dr.

Saada.

In today's lesson, we will be looking at the highest common factors.

Don't worry if you don't know what that is yet, you will, by the end of today's lesson.

For this lesson, you will need a pen and a paper.

So if you do not have these handy, please pause the video and go and grab them and when you're ready, we can make a start.

To start today's lesson, I would like you to have a go at this question.

List the factors of 32 and the factors of 48.

What factors do they have in common? Now try this task should take you about five minutes to complete.

Please pause the video and complete it to the best of your ability.

Resume the video once you're finished.

Welcome back, let's compare our answers.

These are mine.

For 48, my factors are one, two, three, four, six, eight, 12, 16, 24 and 48.

Did you get all of these? Well done.

And for 32, my factors are one, two, four, eight, 16, and 32.

Please mark and correct your work if you need to.

If you look at my diagrams here, I've circled some of the factors.

Why do you think I've circled them? Pretty good.

I circled the ones that are common between the 32 and the 48.

Did you do that too? Let's have a deeper look at this task.

So we've listed the factors of 48 and 32.

We know which factors are common.

I've circled them.

We have a student here saying 16 is the highest common factor.

Do you agree with her? Yes, we do.

If we look at the factors.

The common factors are one, two, four, eight, and 16.

16 is the highest common factor.

We usually write it as the HCF using capital letters.

So if you see HCF, it means the same thing.

The next student here says, I see the factors of 16.

Why is he seeing them? Can you have a little think for me? Really good.

The common factors of 48 and 32, one, two, four, eight, and 16 are actually the factors of number 16.

So 16 is the highest common factor.

And all the common factors are factors of number 16.

In fact, they are all the factors of number 16.

We've not missed a single factor.

Do you think this works every time? Shall we test this? Okay.

Let's find the common factors for two numbers.

Which numbers should we go for? Let's go for 36 and 60.

I would like you to pause the video and list all the factors for 36 and 60.

Then I would like you to circle the common factors.

We will then have a look at the highest common factor and see if all the common factors are also factors of that number.

So if you have the multiples I asked you to do, you should have 36 and all of its factors and you should have 60 and all of its factors.

You can see that 60 has a lot more factors.

Hopefully you've circled the common factors.

So the common factors, let's check if you've got the same ones.

The common factors are one.

Good.

Two.

Do you have that? Three, four, six and 12.

So we have six factors that are common between 36 and 60.

Do you have all of these? Excellent.

Which one is the highest common factor? 12 is the highest common factor.

Really good.

Now let's think about the factors of number 12.

What are the factors of number 12? One and 12, two and six, three and four.

They're all exactly the same factors.

So the highest common factor of 36 and 60 is 12.

All the common factors of 60 and 36, are the actual factors of number 12.

Okay.

So let's write this down.

The HCF the highest common factor of 36 and 60 is 12.

All the factors of 12 are common factors of 60 and 36.

Please pause the video and write this down.

We're going to continue to look at factors with these questions.

So let's read them.

This rectangle has been divided into identical squares.

So we have a rectangle divided into identical squares.

So they're all equals one another.

What is the side length of the square? Now, if you look at the rectangle that has been given to us, what's the width? 48.

How many parts has that side been divided into? So we have one, two, three, four, five, six, 48 divide by six is? Eight.

So each side is going to be 8 cm while we have squares, so this one here must also be 8cm.

It must be an eight by eight square.

Now we can also check using this idea.

So this side is 32.

It's been divided into one, two, three, four equal sides.

32 divided by four, again is eight.

So it has been divided into eight by eight squares.

Okay.

I think these are the largest possible squares.

Do you agree? Are these the largest possible squares that we can divide this rectangle into? Can we divide it into different squares? Have a little think.

Really good.

I can divide it into smaller ones.

I can divide it into slightly bigger ones.

Let's have a look.

If I draw this and I cut it this way.

So if I cut the rectangle in this way.

What have I done? I've created six equal squares with each side being 16 cm.

So I already know that I have another square that is bigger than the one that she has created.

Then we can make bigger ones than 16 what do you think.

Let's have a look at all the squares that we can create from this rectangle.

Okay.

And then we will be able to answer this question.

So if I take this rectangle I can cut into two by two squares, right? So I can cut it into squares that have side length of two.

I know that I can do that because 48 and 32 are both multiples of two.

And I know that because two is a factor of 48.

Can I have any other squares? Well, you know what? I can have a square with a side length of one.

I can have a square, we said side length of two.

I can have a square that has a side length of four.

Look at it carefully the 48 I can divide it into equal parts where each part is four.

And I can do the same with the 32.

I can obviously do a square that has a side length of eight and I can do the 16.

Now, what is common about all of these numbers? One, two, four, eight, 16.

What is this so special about these numbers? Excellent.

They are all factors of 48.

They are all factors of 32.

They are common factors of 48 and 32.

So I can divide this rectangle into smaller squares provided that I am using the factors, the common factors of the length and width of the rectangle.

So now if I give you a different rectangle with different length and width, you should be able to tell me what size squares you can divide it into just by looking at the common factors of the two numbers.

It is time for you to have a go at the independent task.

You have five questions to answer.

If you need help while you're doing the questions, you'll need to refer back to the examples that we have done earlier on during the video.

The independent task should take you about 15 minutes to complete.

So please pause the video and complete the task to the best of your ability.

Resume the video once you're finished.

Welcome back.

How did you get on with the independent task? Really good.

Come on.

Let's mark and correct the work together then.

List all the common factors of 30 and 42.

What did you write down? Come on say it to the screen.

Really good.

So the common factors are one, two, three, and six.

What is the highest common factor of 30 and 42? Excellent it's six.

Find a different pair of numbers with the same highest common factor.

So find another two numbers that have a highest common factor of six.

What did you write down? There are multiple of options.

Okay.

I have 18 and 12.

They have the highest common factor of six.

If the highest common factor of two numbers is 30, list all the common factors.

So the highest common number is 30.

I'm telling you what these numbers are.

What are the common factors of those two numbers? Do you remember this? Excellent.

So the highest common factor is 30.

Therefore the common factors are, all the factors of number 30.

So all we have to do is list the factors of number 30.

And that is one, two, three, five, six, 10, 15, and 30.

Did you get that right? Excellent job.

Well done.

Okay.

And question number five.

What size squares has this student split the rectangle in to? And I've given you a rectangle and this time, the length and the width are 36 and 54.

If we look at what the student has done here, the student has split the 54 into how many equal parts? One, two, three, four, five, six, seven, eight, nine, and 54 divided by nine is six.

So we know that one side length of the square is 6 cm.

Obviously the square has equal sides.

So other sides need to also be 6 cm.

We can check that by checking how many equal parts the 36 has been divided in to.

Just double check that we've not made the mistakes.

That's one, two, three, four, five, six, 36 divided by six is six.

So the student has split the rectangle into squares of side length six.

Okay.

Now what other squares can you split the rectangle into? What did you write down? Come on.

Really good.

Okay.

So the factors of 36 are one, two, three, four, six, nine, 12, 18 and 36.

Hopefully you've listed these down.

The factors of number 54 are one, two, three, six, nine 18, 27 and 54.

Now the common factors are one, two, three, six, nine, and 18.

Which tells me that I can have squares that have the side length of one, squares that half side length of two, squares that have side length of three, squares that have side length of six, squares that have side length of nine and squares that have side length of 18.

And that will be the largest square that we can form.

Did you get that right? Really good.

If you didn't, please make sure that you pause the video and you correct your work as we go along.

This is really really important for your learning.

And what I have noticed with questions like this is when students make a mistake, they usually make a mistake because they missed one or two of the factors.

So make sure you're really careful when you're listing the factors.

And our explore task.

Decide if the following always, sometimes or never true.

If the HCF, the highest common factor is 12, then four and three are common factors.

If four and three are common factors, then the HCF is 12.

If you're feeling confident about this, please pause the video now and have a go at it.

If you need help, I'll be giving you help in three, in two and in one.

Okay.

So I want you to think about what we have done and discuss it during today's lesson.

When I asked you to pause the video and try and write down the factors of two numbers, and we wanted to make an observation there, We wanted to see a relationship between the highest common factor and the common factors.

You did that in your book.

And then I asked you to copy down the sentence there.

If you refer back to that, that should help you.

For the second statement, I want you to find a pair of numbers that have four and three as their common factors.

Then find the HCF.

Is it 12? Is it not? Now find another pair of numbers.

Find another two numbers that have four and three as their common factors.

And then check what is the highest common factor? Is it always 12 or not.

With this is little hint you should be able to have a go at this.

Please pause the video and have a go at the explore task.

You need to spend roughly 10 minutes on it trying with lots and lots and lots of numbers.

Resume the video once you're finished.

Welcome back.

How did you go on with the explore task? What did you write down for the first one? If the HCF is 12, then four and three are common factors.

Excellent.

Very good.

It's always true all the factors of 12 would be common factors if HCF is 12.

Next one, if four and three are common factors, then the HCF is 12.

Is that always sometimes or never true? What did you write down? I wonder how many numbers you've tried.

How many pairs of numbers you tried.

Okay.

Sometimes 12 will be a common factor but not necessarily the highest common factor.

For example for 180 and 240, 60 is the highest common factor.

Not 12.

Did you get that? Really good.

This brings us to the end of today's lesson.

You've done some fantastic learning.

So well done.

Please remember to complete the exit quiz to show what you know.

This is it from me for today.

Enjoy the rest of the day and I'll see you in the next lesson.

Bye.