Lesson video

Hello, I'm Mr Langton.

And today we're going to be looking at Prime Factorization.

All you're going to need is something to write with and something to write on.

Try and find a quiet space where you won't be disturbed.

When you're ready, we'll begin.

We'll start with the try this activity.

Filling the gaps below.

Try to find more than one way.

Pause the video and have a go, when you're ready unpause it we can go through it together.

You can pause in three, two, one.

How did you get on? I hope that your first step was one of these three.

I'mma go through each one now write them down.

So two multiplied by 18, could be written as two multiplied by three times six, now two and three are already prime numbers, we can't break those down.

Six can be broken down into two times three.

12 multiplied by three is 36, so we know that three is already prime and we could have four times three, which gives me two times two, times three, times three.

Another way that we could do it, we could say that four is two multiplied by two multiply that by nine, it gives me two, times two, times three, times three.

So can you see in each case, we've got two, two is multiplied together and two, three is multiplied together, writing in index form, Where actually just two squared, times three squared equals 36.

Did you get one of these methods? Did you get different one? It's one that I missed out, and that would have been six times six is 36.

I'm not going to break that down because we can see here, that ended up with, two times three, is six and two times three is six.

So no matter which way you break down 36, once you get down to just the prime factors, you always get the same answer.

And that's the same for every number that you try and break down.

Every compounding digit can be written as a product to prime numbers.

Now our compound integer, is actually just a number that's not prime, it's a number that's made by multiplying all the numbers together.

And we've got here is two different examples, how it could break down 30 into a product to it's prime factors.

What's the same and what's different.

The one on the left, broken down is two lots of 15 and then to three lots of five.

So in the diagram, well I've actually got, I just put some bubbles around here.

I've got two lots of this, haven't I? So I've got two lots, of three lots of five.

Each of these bubbles has got three lots of five in it.

On the right hand side, I've got three sets here.

Each of these sets is five lots of two.

So I've got three lots, of five lots two.

And again it represents the same thing, It's another way of representing 30, but that's it, there are lots of ways of breaking it down.

When we write numbers out, as products of prime factors, it's good practise to put them in order from smallest to largest when multiplying them together, you don't have to, it's not wrong if you don't, it's just nice to do it, it just looks a little bit simpler.

Now one last example from me, express 80 as a product of its prime factors.

I'ma start off writing 80 at the top of the page.

I'ma split that up into two numbers, ending in a zero, so I know that 80 is a multiple of 10, let's say it's eight multiplied by 10.

Now I can make eight by doing four multiplied by two, now two is a prime number, we have a circle around that, because I know I can't break that down anymore, Four on the other hand is not a prime number.

I will make four, that is, two multiply by two, Now I've reached the end of those brunches I can't go any further, what I haven't done is focused on the 10, 10 can be made up of two, which we've already said is a prime number, multiplied by five, which is also a prime number.

So the product is prime factors, two, times two, times two, times two, times five, and that makes it 80.

Now can write that in index form, if I multiply four twos together, then it's two to the power of four, multiplied by five equals 80.

So expressed 80 as a product of his prime factors.

Now it's your turn.

Pause the video and access to the worksheet.

When you finished unpause it, and we can go through it together.

Good luck.

How did you get on? Let's go through the answers now.

So in the first case 36 is something multiply by 12.

So we're break 36 down, we've got three lots of 12.

12 is made up of four lots of three, four is made up of two multiplied by two, excuse me, two, times two, times three, times three, which is two squared multiplied by three squared.

90 which is broken to nine times 10.

Nine is three times three, 10 is two times five.

Well I write them in order, two, times three, times three, times five, which is two multiplied by three squared multiplied by five.

42 is seven lots of six and 62 lots of three.

So 42 equals two, times three, times seven.

And 60 has been broken down into six times 10, which is two times three, and two times five, excuse me, two, times two, times three, times five, which is also two squared, times three, times five.

Now in question two, we've not given you the prime factor trees this time, so it's time to you to break it down and have a go.

So in the case of 72, that would be two cubed, times three squared, two cubed is eight, three squared is nine, eight times nine, 72.

For B, the answer is two to the power of four multiplied by three, multiplied by five.

And I'm just curious, did you do a prime factor tree for 240 and break it down or did you do one for 24 and break it down and one for 10 and break down and then recombine them then.

Because that second method might've been easier.

175 is five squared which would be 25 multiplied by seven.

And 50 squared, just again, still a bit curious, did you multiply out first or did you start from the 50 squared? If I start from 50 squared, that must be made up of 50 times 50.

And 50 is 25 times two, and 25 is five times five.

So altogether I've got two squared, multiply by five to the power of four.

I will finish that off for you to so you can see.

Okay.

Question three.

A is half the size of B, true or false.

So let's have a look.

A is two multiplied by three squared multiplied by five squared.

So we've got three squared, multiplied by five squared, this case we've got two squared, whereas here we've only got a two.

So if I took A, two, lets write it out, three times three, times five times five.

If I take B, is two squared, I'ma try line everything up now, times three squared, times five squared.

So can you see how everything matches up, makes it that the B got an extra two, so B is going to be twice as big as A, which means A is half of the size of B.

So it's true.

Finally, the diagram on the left shows a representation of 60.

Can you complete the prime factor tree to show this? How many other ways can you represent 60? Pause the video and have a go, when you're ready, we'll go through it together.

You can pause in three, two, one.

So let's have a look at one away to go.

Initially, we've got five of these large circles, haven't we? So we've got five lots of something, inside each of these lots, altogether we've got 12 little circles and we know that five times 12 makes 60, so that's good, so let's take one of these little circles, I expanded a little more, les draw it out, duh, duh, duh, duh, that's the four squares inside there, so we broke part out, now there are three bits inside there, one, two, three, there are three lots, and inside each of those lots, is four, and inside that four, we've got two lots of two.

So that's how that diagram is represented as a prime factor tree.

Hopefully you can use other ways as well.

We're going to leave it there for today.

I'll see you later, goodbye.