Lesson video

- Hello, and welcome to another video.

In this lesson, we'll be looking at prime factors.

I am Mr. Maseko.

Before you start this lesson, make sure you have a pen or a pencil and something to write on.

Pause the video here if you need to get those things.

Okay, now that you have those things, let's get on with today's lesson.

Try this activity.

So pause the video here and give this a go.

Okay, now that you've done this, let's see what you've come up with.

Well, we are told 14 has exactly two prime factors.

What could prime factors be? Well, factors that are prime numbers, and those are two and seven.

How many other numbers can you find with exactly two prime factors? What did you come up with? Well, you could have had 10 because the prime factors for 10 are two and five.

What other number could you have had? Well, you could have had 15.

The prime factors of 15 are three and five.

How many prime factors does 12 have? Well, 12 has two prime factors, which are what? Two and three.

Now, 12 does have other factors.

So, 12 has the factors four, six, 12, and also one, but two and three are the only factors that are also prime numbers.

And the same can be said for 10 and 15.

There are other factors, but these are the only factors that are prime numbers.

And that's what we're gonna be looking at in today's lesson.

So when we think about prime factors, we are thinking about factors that are prime numbers.

So let's write this down so we don't forget.

So these are factors, and here we are.

Okay, so what's the smallest number with two prime factors? Well, let's look at the smallest prime number.

Well, the smallest prime number is what? What's the smallest prime number? That is, good, two.

What's the next smallest prime number? That is three.

Well, if we multiply these together, two and three gives us six.

Two multiplied by three gives us six.

The smallest prime number with two prime factors is six.

What about three prime factors? And what about 10? Pause the video here and see if you can figure this out.

Okay, let's see what you've come up with.

For the smallest number with three prime factors, see how we found the smallest number with two prime factors? We multiply the two smallest prime numbers.

So what about three prime factors? We can do the same thing.

So two multiplied by three multiplied by five, which would give us what? 30, good.

Now, I can see some of you saying, but sir, what if I just do two times two? That gives me four, and that's smaller than six.

But how many prime factors does four have? You've got it.

It only has one prime factor because two is repeated and we're looking for a number with two prime factors, distinct factors.

Same thing for three prime factors.

So what would you have come up with for 10 prime factors? Well, you could have just done two, multiply it by three, multiply it by five, multiply it by, what's the next prime number? Seven, all the way up to the 10th prime number.

So what is the 10th prime number? Well, that is 23.

When you multiply all of those, you get the smallest number with 10 prime factors, and it's a really big number.

Let's explore this a bit further.

Here's an independent task for you to try.

Pause the video here and give this a go.

Okay, now that you've tried this, let's see what you've come up with.

These are all the factors of 18.

These are all the factors of 49.

These are all the factors of 100.

And these are all the factors of 60.

Now, how many prime factors do those numbers have? Well, all these numbers have two prime factors.

Remember, we've already seen this.

The smallest number with three distinct prime factors was 30, which you get by doing two multiplied by three multiplied by five.

And the smallest number with four prime factors is 210, two multiplied by three multiplied by five multiplied by seven.

It's 210.

So for this task, I want you to list the prime factors of every number between two and 30.

What do you notice? Of every even number between two and 30, what do you notice? Why is two the only prime number? And then write other numbers as a product of prime numbers.

Pause the video here and give this task a go.

Okay, let's see what you've come up with.

Well, two only has one prime factor, which is two.

Four also only as one prime factor, which is two.

Six has two prime factors, which are two and three.

Eight only has one prime factor, and that is two.

10 has two prime factors, which is two and five.

12 has two prime factors, which are two and three.

14, two and seven.

16 only has one prime factor, and that's two.

18, well, that has two prime factors with two and three.

20, well, that has two prime factors, which are two and five.

22, well, that's two and 11.

24, that's two and three.

26, that's two and 13.

28, well, that's two and seven.

And then 30.

That is two, three and five.

What do you notice? What do you notice? Every even number between two and 30, every even number has a prime factor of two.

Every single even number has a prime factor of two.

So if you ask this question, why is two the only even prime number? Because, well, every even number after two will have a factor of two.

That's why it's called an even number, because it has a factor of two.

That is why two is the only even prime number.

Now, this student says, "I can write 12 as a product of prime numbers," so two times two times three.

So two multiplied by two multiplied by three.

Is there any other number you could have wrote using only prime numbers? Well, you could have done 30.

We've done 30 already, which was two multiplied by three multiplied by five.

Any other number? Well, let's look at the number 18.

Well, 18 has what? Two and three as prime factors.

So we could write two times three, that's six.

12 times three.

Now that's 18, which is a product of prime numbers.

Is there any number that can't be written as a product of primes? The answer to that is no.

Every single number can be broken down in this way and written as a product of only prime numbers.

And you'll do more of this later on in your school career.

Well, that's it for today's lesson.

Thank you very much for taking part.

I will see you again next time.