Prime Factors LCM HCF – GCSE Maths Revision

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What you need to know

What you need to know:

Firstly, we define a factor of a given number to be anything that that number is divisible by. For example:

1, 2, 3, and 6 are all the factors of 6.

Furthermore, we define a prime number as any number greater than 1 that has only two factors: itself and 1. So, 5 is a prime number, since its only factors are 1 and 5. However, the number 6, as mentioned, is divisible by 2 and 3 as well as 1 and 6, so it is not prime. We call the number 6 a composite number.

Note: it would be an impossible task to learn all the prime numbers off by heart: there are infinity of them. As a result, it’s important to understand what they are so to be able to spot one. However, it is useful to become extra familiar with the first few, say: 2, 3, 5, 7, 11, 13, 17, as these are likely to appear a lot.

It follows naturally that we define the prime factor of any given number to be any factor that number has that is also a prime number. Consider the number 10, for example. 10 is divisible by 1, 2, 5, and 10. Clearly 10 is not prime (it is divisible by 5 and 2), and 1 is also not prime (only numbers greater than 1 can be prime), whereas both 2 and 5 are prime. Thus, 2 and 5 are the prime factors of 10. Moreover, we say that the prime factorisation of 10 is 2 \times 5 .

Every whole number you can think of has a unique prime factorisation, and one way of finding what that is is to use a factor tree. To do this, write your number of choice in the middle of the page (see the picture below for an example using 60).

Then pick any two numbers (importantly, numbers that are not equal to 1) that multiply together to make your number, such as 6 and 10, and draw diagonal lines connecting you first number to them. [Note that if there’s no way to factorise your number like this, then voila: your number is prime.]

Carrying on, perform the same step to our new numbers: 6 and 10, and if either of them turn out to be prime, put a circle around them. In this case, they don’t, and we can split 6 and 10 into:

2 \times 3 and 2 \times 5

We would perform the same repeat step to all these numbers, but as it happens they are all prime, so we simply put a circle around them all. As there is nowhere to go, that means we have completed our factor tree, and determined that the prime factorisation of 60 is:

2 \times 2 \times 3 \times 5.

Prime Factors LCM HCF Revision and Worksheets

HCF LCM Product Of Primes
Level 4-5
BIDMAS and Prime Factors
Level 4-5
LCM HCF Factors and Prime Numbers
Level 4-5
Factors Multiples Primes
Level 4-5
Common multiples and LCM
Level 4-5
Common factors and HCF
Level 4-5

The prime factor worksheets on this page are designed to help students and tutors to get access to the best revision materials. Whether you are revising prime factor trees, HCF or LCM, you will find worksheets and questions to help you.

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