 # Recognise Prime Numbers

In this worksheet, students will practise identifying prime and composite numbers, so that these facts can be used to solve complex problems and mental computations quickly. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Number Operations and Integers

Curriculum subtopic:   Structure and Calculation, Whole Number Theory

Difficulty level:   ### QUESTION 1 of 10

Prime numbers are some of the most useful numbers in maths and they can help you out a lot!

Therefore, it is a really good idea to understand how to identify them and to commit, at least the most common ones, to memory.

Definition: A prime number is a number that only has two positive factors.

What this means in reality is that you can only divide a prime number by two things: 1 and itself.

So 17 would be a prime number because you can only divide it by 1 and 17.

But 15 wouldn't be a prime number because you can divide it by 4 things: 1, 3, 5 and 15.

Numbers that aren't prime numbers are called composite numbers.

What are the most common prime numbers?

You are expected to know the prime numbers up to 30, so you need to memorise this list:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

In this activity, you will practise identifying prime and composite numbers so that you can use these facts to help you solve complex problems and mental computations quickly.

A prime number is a number that can be divided by how many factors?

Use the information you have learnt in the Introduction to complete the sentence below.

Is the number below prime or composite?

24

Prime

Composite

Is the number below​ prime or composite?

17

Prime

Composite

Is the number below​ prime or composite?

25

Prime

Composite

Match the numbers below to the definition which best describes each.

## Column B

1
Prime
3
Prime
8
Composite
9
Neither prime or composite
23
Composite

Which of the numbers below are primes?

1

3

7

10

15

29

Which of the numbers below are composite?

1

3

7

10

15

29

Two prime numbers have a difference of 27.

Which two numbers are they?

1

3

7

10

15

29

True or false?

1 is a prime number.

True

False

• Question 1

A prime number is a number that can be divided by how many factors?

2
Two
EDDIE SAYS
This fact is the heart of the definition of a prime number. Primes only have two factors: 1 and the number itself. So 3 is a prime number, as its only factors are 1 and 3. Whereas 4 is not, as its factors are: 1, 2, 4. Do you see how identifying the factors of a number is the key consideration when recognising primes?
• Question 2

Use the information you have learnt in the Introduction to complete the sentence below.

EDDIE SAYS
Numbers which aren't prime are called composite. The only positive number that isn't either prime or composite is 1 - as it does not meet the definition of a prime (as it only has one factor), but is also not composite.
• Question 3

Is the number below prime or composite?

24

Composite
EDDIE SAYS
24 can be divided by: 1, 2, 3, 4, 6, 8, 12, 24 It has more than two factors. Therefore, it's a composite number.
• Question 4

Is the number below​ prime or composite?

17

Prime
EDDIE SAYS
17 can be divided by: 1, 17 It has only these two factors. So it's a prime number. Decimal numbers are not acceptable as factors, so you could not, for example, reason that 17 is not prime as it has factors of 2 and 8.5.
• Question 5

Is the number below​ prime or composite?

25

Composite
EDDIE SAYS
25 can be divided by: 1, 5, 25 It does not have as many factors as 24, but it still has more than two. Therefore, it's a composite number. Watch out for square numbers, as these can never be prime. Square numbers are products of numbers which are multiplied by themselves e.g. 9 (the square of 3), 16 (the square of 4), etc.
• Question 6

Match the numbers below to the definition which best describes each.

## Column B

1
Neither prime or composite
3
Prime
8
Composite
9
Composite
23
Prime
EDDIE SAYS
The numbers which are composites must have another number, apart from 1 and itself, which they can be divided by. 8 can also be divided by 2 and 4. 9 can also be divided by 3. 3 and 23 are prime numbers, as they can only be divided by themselves and 1. It's that tricky question again. Is 1 a prime number? No. So is it a composite? No. 1 is the only number which is defined as neither prime or composite. Well done if you remembered that fact.
• Question 7

Which of the numbers below are primes?

3
7
29
EDDIE SAYS
Remember that the primes can only be divided by themselves and 1. 10 and 15 both have more than two factors, e.g. 15 has factors of: 1, 3, 5, 15. Are you feeling more confident? This is an important foundation to understand, in order to build on it in other areas of your maths skills.
• Question 8

Which of the numbers below are composite?

10
15
EDDIE SAYS
Remember that composites can be divided by at least one other factor, apart from themselves and 1. e.g. 10 has factors of: 1, 2, 5 and 10. Did you fall into the trap and choose 1? Watch out for this and remember that 1 is the only number which is neither prime or composite.
• Question 9

Two prime numbers have a difference of 27.

Which two numbers are they?

EDDIE SAYS
If the difference between two primes is odd, this means one of the numbers must be even and the other must be odd. The only even prime number is 2 so we know this must e one of the numbers in question. To find the other number, we can calculate: 2 + 27 = 29 This was a tricky question so don't worry if you did not spot this straight away. This is a good example of how knowledge of prime numbers can be used to solve a problem.
• Question 10

True or false?

1 is a prime number.

False
EDDIE SAYS
It might seem like this question keeps cropping up, but this but is a really important fact and one which students often get confused. 1 is not a prime number because it only has one factor. Prime numbers must have 2 factors only - no more, and no less! Great work completing this activity! Try listing all the prime numbers to 30 from memory a couple of times before you move on.
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