Lesson video

I'm Mr Lund and in this lesson, we're going to be using prime factor decomposition, okay? Hi everyone, being able to use numbers in prime factorised form and been after easily convert between that prime factorised form, and their integer solutions is a useful skill.

Here I have four times by five and that equals 20.

What do you notice about the second example? Did you see it is twice the size? Two to the power of three times by five equals forty.

We can use numbers in prime factorised form to help us work out calculations with other types of mathematical operations.

Here I have 672 over 32.

If I write that in prime factorised form, here's what I'd have.

I can see that two to the power of five will cancel in the numerator and the denominator, leaving me with just three times by seven, that equals 21.

I've quickly managed to work out that 672 over 32 is equal to 21.

Let's look at a second example.

Can you see which terms are common that are going to cancel? That leaves me with two times by three, which is equal to six.

You have some examples for you to try pause the video and return to check your answers.

Here's the solutions to questions one and two.

In question 2B and 2D, both of those solutions were incorrect, they were false.

Here are the correct solutions.

I'm going to use a function machine to show you what happens when we multiply numbers in prime factorised form.

If I wanted to double this number, then my output looks almost identical, but look, now I have two raised to the power of two.

Look at this, the same input made seven times larger.

Will find something that looks almost identical, but now seven is raised to the power of two instead.

Let's use the same input one more time, and let's multiply our number by 14.

Now 14 can be written in prime factorised form as seven multiplied by two.

Can you guess what the output is going to be there? There two and seven have been raised to the power of two, 11 was already raised to the power of two.

When we write numbers in prime factorised form, we can also easily find the factors of that number.

Here I'm going to show you some of the factors of two times by seven times 11 to the power of two.

Notice all the factors are common elements.

In these two examples, notice that the powers are greater than what is available in our original number.

So these two numbers are not factors.

Some questions for you to try pause the video and return to check your answers.

Here's the solutions to questions three and four.

Now questions three and four, hopefully you're starting to understand the power of using numbers in prime factorised form.

Three to the power of three in question four, three to the power of three, does not go into our original number.

Because we have in our original number, we had three to the power of two, which is nine three to the power of three is 27.

It is not a factor of that number.

Let's have a look at what happens when we square numbers in prime factorised form.

Look at this pattern.

Do you see when we square numbers in prime factorised form, the powers are doubled.

Now, if we square a number, the powers double.

Conversely, if we take the square root of a number, the powers will be halved.

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

These questions five and six, now question five when we square numbers in prime factorised form we're going to double the powers.

One way of taking the square root of numbers in prime factorised form you halve the powers.

So my question to you is, if I were to take the square root of, let's say this expression here, it's in prime factorised form.

What happens to the three.

Now remember that three is three to the power of one, can't quite see that it's three to the power of one.

So halving the powers would give me that.

You could also write it to look like this.

They you go get a break from my ugly face.

Well done for getting this far pause the video, and check your answers and I will give my own.

Here is the solutions to question seven.

If like me, you're really tired, then maybe you should take a bit of a break.

Maths is like that, sometimes if you're doing difficult maths, you just need to pause.

It won't all come to you in a second.

Take a break, take some time out and think about what you've been doing at a later date.