Lesson video

Hi, everyone.

I'm Mr. Lund, and in this lesson, we're going to be looking at prime factor decomposition.

Some of you might just know this as factor trees.

It's stuff that you should have seen before during your secondary career.

Hi, everyone.

Prime numbers are the building blocks for all other numbers.

All numbers can be displayed as the product of their prime factors.

Do you notice in these three calculations, all the numbers are prime numbers? Finding their products will find integer solutions.

We can display the product of prime factors in index form.

Here, can you match the number cards with their index form? Let me help you.

Remember, these find integer values, so two to the power of two times by five is just like saying four times by five, which equals 20.

Three to the power of three equals 27, and two times seven times 11 to the power of two is 1,694.

Here's some questions for you to try.

Pause the video, and return to check your answers.

Here's the solutions to question one.

To be able to move between the prime factorised form of a number and its integer solution or its product is a really useful skill, something you can practise.

Prime factor trees are one method to help us find the product prime factors of any number.

Here's the number 20.

I'm going to start by dividing this number by a prime number, and then I'm going to find its factor pair.

I'm going to circle a prime number, and then turn my attention to the number that is not prime.

What are the factor pairs of 10? Two and five are both prime numbers.

So the product of prime numbers of the number 20 is two multiplied by two multiplied by five.

Here's that number in index form.

Let's have a look at the number 27.

Let's divide the number 27 by a prime number and find its factor pair.

Circle the number which is prime, and turn your attention to the number that is not prime.

What are the factor pairs of nine? There we go.

They are both prime numbers.

So the product prime factors of the number 27 can be written like so, and in index form it would look like this, three to the power of three.

Here's another number that we have looked at previously written in a prime factor tree.

Don't worry too much if you don't divide your number by a prime number to start.

Let's look at the number 20 again.

I'm going to divide it by four and find its factor pair, which is five.

Five is prime, so I'm going to circle it.

Four is two times by two.

The factor pairs of four, two and two, they're both prime.

Let's circle our primes, and we see that the product of prime factors does not change.

That is why prime numbers are sometimes known as the building blocks of numbers.

Here's a question for you to try.

Pause the video, and come back to check your answers.

Here's the solutions to question number three.

Hopefully you got on with this okay.

It's a nice little easy start to get your brain manoeuvring into using factor trees.

So can you match the factor trees to their correct expressions in index form? Pause the video, and return to look at your answers.

Here's the solutions to question number four.

Now in question number four, 56 is eight times by seven, but remember eight times by seven is not in the prime factorised form, okay? Here's the final questions.

Pause the video, and return to check your answers.

Here's the solutions to question five and six.

I want to show you a different technique whilst I can of finding the prime factorised form of the number 105.

Here, if I divide 105 by a prime number, I'm going to use five.

Then five goes into 105, 21 times.

From there, I can divide 21 by a prime number.

Don't forget to circle the primes.

Three goes into 21, seven times.

Let's circle all my primes.

And there we go.

In prime factorised form, 105 is three times by five times by seven.

This is a really nice method, and I think a little bit quicker than factor trees.