Lesson video

Hi again everyone.

And welcome to today's lesson.

Today's lesson is going to be on, to understand and use the terms 'common factor' and 'common multiple'.

Okay, so if we're ready, we're going to get started.

Now let's have a quick look before we go too far into it about what we're going to do in today's lesson through the agenda.

So the first thing we're going to do is, we're going to try and define multiples and factors.

Then we're going to try and find common multiples.

Then we're going to look at common factors and then you guys can have an independent task kind of test and see if you've understood that properly.

Okay, before we get started, just make sure that you've got a pencil and a piece of paper so you can make some notes.

If you don't have that, pause the video and get it now.

Okay, so the first thing we need to do is try and define multiples and factors.

So before I taught you about this, if you've got an understanding already, maybe pause the video now and try and write your own definition of what you think a multiple is, what you think of factor is, and think about what's the same, what's different about them from what do you know already.

Okay, so pause the video now and then play when you're ready.

Okay, so let's have a look and try and define multiples and factors.

Well a multiple, is the result of multiplying a number by an integer.

Now that's lots of complicated.

So let's put some examples in.

So for example, 12 is a multiple of three because it's in the three times table, essentially.

So three, six, nine, 12.

So three multiplied by four is equal to 12, therefore 12 is a multiple of three.

Can you tell me another multiple of three? Yep, it could be anything.

So just shout one out.

Great, okay.

So, if you can think of some more, try and think about what makes them a multiple, well, if they're in that times table, no matter how far up then they are a multiple of that number.

So, what's different about a factor then? Well a factor, is a number that divides into another number exactly and without leaving a remainder.

So giving you some examples of maybe that, make a little more sense.

Essentially, a factor is a part of something that will make a product.

So, two numbers that multiply together to make another number, one of those numbers is going to be a factor.

Let me give you an example of that, so eight is a factor of 24 because eight multiplied by three is equal to 24, there is no remainder.

So both eight and three are both factors of 24.

So a good way to think about factors is they're going to come in pairs because you need to multiply two numbers together.

Now there is a bit of an exception to that rule, we will talk about that in another lesson.

Oh, thinking about 24, can you give me any other factors of 24? We said eight and three, can you think of any others? Yep, okay, great.

So we could start with one and 24, they are factors of 24.

We could have two and 12.

We could have three and eight.

We can have six and four.

Okay, great.

So let's move on then.

So we've gone through the definition now, let's go into a bit more detail.

But how do we go about finding multiples? Well, the easiest thing to do, if you know your times tables, then you know your multiples, it's that easy.

So thinking about ways that we can do it, well, simply writing down our time tables is a great way of doing it.

So let's a start nice and simple.

We're think about multiples of three.

Well writing down my timetable is going to give me all my multiples of three.

So nice and simple.

Likewise, if I've got my multiples of four, I simply need to write down my times tables again.

So as we can see them there all written down.

Great.

Now, having a look at this, what we're looking at today is I want to think about something called a common multiple.

Now what that means, a common multiple means it's found in both.

So I want to look for a common multiple of three and four.

So something which is in the three times table and in the four times table.

Now I've written them all out for you.

Can you see any which are common multiples there? Have a look, pause the video if you need to and see which of these you can find a common multiples.

Okay, great.

12 we can see is a common multiple.

We can see that 24 is a common multiple.

Now as we go up, if we were to go on further multiples, we could obviously find more.

Do you spot any pattern there? Yeah, that's right.

So 12 doubled is 24.

And that does make sense because if you've got common multiples and then we doubled them all they're still going to be our common multiples.

Okay, now you turn then.

I'm not going to write anything down for you.

I want you to pause the video now and then find me some common multiples of both two and six.

Okay, so how did you do? How many did you find? Great.

Let's have a look then and double check.

So, the first thing I'm going to do is I'm going to write down my multiples of two, write down my multiples of six, and then I'm looking for the common multiples.

Now, I don't know how enthusiastic you were and how far you went with your multiples, but hopefully to a certain point you then start to see a pattern.

You realise that you can just double it and things, and notice the ways that we can find the common multiples.

So let's have a look of just some of the examples you could have had.

Well six.

You could have had 12.

You could have had 18.

Hold on a minute.

Look at those multiples of six.

We've already said that six is a common multiple 12 is a common multiple 18 is a common multiple.

What about 24? Yeah.

So 12 multiplied by two would be equal to 24, so that would be a common multiple as well.

So we're noticing essentially that all of the multiples of six are also multiples of two.

And why is that? Yeah, so obviously they're all going to be even numbers, so they are going to all be multiples of two.

Okay, so that's a nice little thing to kind of unpick further.

And it's a really good, when we look at things like common multiples and factors, always keeping our eyes open for mathematical thinking, looking for patterns wherever we can.

Did great.

Let's move on then, that's common multiples.

I think that's pretty clear.

We should be pretty happy with that.

Let's have a look at how we go about finding factors.

Now you may have done this in previous years, so the way we try and do it, the way I try and do it, to make sure I'm being as systematic as possible and not mixing any, is I use something called a factor bug.

Now a fact of bug is simply just a great way of finding factors of something.

The first thing I do, is I draw myself a little bug.

Now I'm not much of an artist as you can tell.

And then whichever number I'm trying to find out the factors for am then going to put it in the head.

Then I can go about trying to find all the different factors.

Now it's really important when we're finding factors, particularly when we get to larger numbers that we make sure we do it systematically.

Now, when I say systematically, I mean, we need to do it in a clear order.

So I'm going to try and do it as systematically as possible.

So where should I start? Yeah, great.

The first thing I want you to do is a one and 24.

So one multiplied by 24 equals to 24.

And this, the antenna of the bug is always going to be there because every number will have the factors of one and itself.

Okay, they're always going to have it.

So every number this a great place to start.

Then I'm looking, what's my next one? Now you can see that along here I've got one.

So I'm going to be systematic and I'm going to see what I know it's an even number.

So I'm really hoping it's got a multiple, it's got two as a factor as well.

Then, two multiplied by 12 is equals 24.

Now it's three.

Yeah, good.

So three and eight.

Now four my next one, four multiplied by six.

Multiply any more, five, oh no, five, isn't a factor of 24.

Cause five, 10, 15, 20, 25, and that is not.

And then you can see by being systematic.

Well, I'm back round to six then, and I've already done six, so I don't need to carry on, go.

So I know by being systematic that I found all the factors of 24.

Now, I've got an example up here, cause it's something to think about.

If we have a special type of number, for example a square number.

You'll notice that we have our antenna here, one and 36, we've got two and 18, three and 12, four and nine.

And then, what I've got here.

So if I got six, six multiplied by six is equal to 36, but I don't put six in twice.

Cause it's still just the one factor.

So if we have square numbers, where a number multiplies by itself to make that number, then we're actually going to have an odd number of factors.

So it makes a square numbers a little bit special.

So with the square numbers, we like to think of a square number has got this, we put it in the bottom and we call it a stinger.

Okay, so it has a stinger at the bottom.

So that's a good way of differentiating it from our normal type of numbers, now, you may also find numbers where, the only fact is you have a one in itself and they're going to be what we call our prime numbers.

And we'll look at those in a separate lesson.

But actually they become what we call a factor slug, instead.

That's a nice way of doing this.

A really good way of exploring factors.

Okay.

Looking for the common factors then.

So between 24 and 36, can you see any common factors there? And as, one pretty obvious one is in there.

Yeah.

One is always going to be a common factor, it's kind of a given.

Any other common factors? Well, yeah, exactly.

Great to see is working systematically again, two is obviously going to be a common factor cause they're both even numbers.

Anymore? Go three, four.

We've also got six as a common factor.

Anymore? Okay, great.

So you can see that by working systematically and drawing our factor bugs, it becomes really easy to be able to identify those common factors.

Oh, look, I missed one, can you notice that? Well, what I missed was 12.

Okay, so well done if you were shouting on your screen telling me I've missed one, great job.

So 12 is also one of our common factors.

Great job if you spotted that.

So, the common factors we've got there, one, two, three, four, six, and 12.

Now over to you.

So I've already started your factor bug for 12 and 20.

What I want you to do, is to find me all the common factors and then what's the highest common factor you can find.

So which number is the greatest of the common factors? Okay.

So pause the video now and have a go and then when you're ready, play the video again.

Okay, how did we do? Great.

So let's have a look at some of those then.

We should have had one and 12, two and six, three and four.

Anymore? Nope.

Okay, then 20 would have one and 20 two and 10, four and five, any more than that? Nope.

Okay, the common factors then, we have one obviously, two, four, any more common factors in there? Okay, great job guys.

So common factors of 12 and 20, we've got one, two and four.

And therefore the highest common factor that we have is four.

Okay.

So hopefully we've got the hang of this.

We've got a nice clear structure to be able to help us now.

What I want you to do now, is I've got some questions for you to complete on your worksheets.

So I want you to pause the video, go to your worksheet, complete those questions.

If you need to, come back to the video, to look at the structure, things like the factor bug, using the common multiples to be able to help you to solve those problems. And then when you're ready, play the video again, and we'll go through some of those answers.

Right.

Now hoping that you've may have been able to finish that, so let's have a go at looking at some of those answers.

So some of the colours, some of the factors of 10, we could have had, one and 10, note I'm doing it ina factor pair still, two and five.

18, we could have had one and 18, two and nine, three and six.

25, interesting one, we should have one and 25 obviously and then five multiplied by five.

So we just got five as one factor, because it's one of our square numbers.

So we have an odd number of factors.

Good job if you're able to think about that and notice that.

40, quite a few, one and 40, two and 20.

four and 10, five and eight.

Okay.

Now moving on from factors let's have a look at those multiples.

So the first six multiples, otherwise we could keep on going forever.

If you did choose to go further, great.

So eight, we could have had eight, 16, 24, 32, 40, 48, Great job.

Always good to practise our multiplication tables.

Four, should've had four, eight, 12, 16, 20, 24.

Seven, should've had seven 14 21, 28, 35, 42.

And lastly those nine times tables, nine, 18, 27, 36, 45, 54.

Okay, so those multiples, we're really looking at those times tables.

Okay, great job so far.

Let's have a look, our next question is, write three factors of 40 which also factors of 30.

So this is really where I hope you got those factor bugs out and you're able to try and find those common factors.

Draw enough factor bug.

Hopefully they looked a little bit like mine, and we're looking for three factors of 40 and 30.

So there's common factors.

We should have had one, two, five, 10, anymore? Okay, so we should've had our factors there, so hopefully we were able to pull that up.

Let's have a look at question four.

Zaara has 32 sweets and is able share them equally between her friends.

She has more than five friends but less than 20, how many friends might Zaara have? Okay.

So hopefully even if it's a word problem, you're able to look at this and think about, it as factor bug.

So we're able to look at the factors of 32, because we know she is sharing them equally between her friends.

So how many friends could she have had? Well, the different options are, if she's got eight friends they would have had four sweets each, or she could have had 16 friends that would have each got two sweets.

So well done if you found both of those combinations and you were able to really reason and explain about how that made sense or that was the answer.

Okay, guys, we've done a really good job today, I really love talking about factors with you, hopefully you've learned a really good useful tool today that is going to be able to support you in finding common factors and common multiples.

Now if you'd like to, please ask your parent or your carer to share your work on Twitter for you using those hashtags.

Right.

Before you finish, make sure you go to that quiz.

It just helps you to consolidate and review the learning that we've been through today.

Thank you very much, guys.

Done a great job.

And I'll see you again soon.

Bye bye.