What Is a Prime Number? Explanation and Practice Questions for Primary Parents

A prime number is a number that can only be divided by itself and 1 without remainders. Here we explain what exactly this means, and provide you with some practice prime number questions to test your child with.  

This blog is part of our series of blogs designed for parents supporting home learning and looking for home learning resources during the Covid-19 epidemic.

What is a prime number?

Prime numbers are numbers with only two factors – themselves and 1. This means they cannot be divided by any other numbers without leaving a remainder.

13 is an example of a prime number – it can only be divided by 1 and 13. Dividing by another number results in numbers left over e.g. 13/6 = 2 remainder 1.

What are some example prime numbers?

There are 8 prime numbers under 20: 2, 3, 5, 7, 11, 13, 17 and 19.

2 is the only even prime number – all other even numbers can be divided by themselves, 1 and 2 at least, meaning they will have at least 3 factors.

1 is not a prime number, because it only has 1 factor – itself!

Prime numbers can continue well past 100. For example, 21,577 is a prime number.

When will my child learn about prime numbers in primary school?

Prime numbers are not introduced in the UK until Year 5.

According to the National Curriculum, Year 5 children should be taught to

“know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers to establish whether a number up to 100 is prime and recall prime numbers up to 19.”

In Year 6, children should be able to “identify common factors, common multiples and prime numbers”.

How are prime numbers used in the real world?

One of the most important uses for prime numbers is in cyber security – making information shared over the internet safer.

In order to encrypt (make secure) things like credit card details, medical records, even some messaging services like WhatsApp, software engineers make algorithms using prime numbers.

By multiplying two very large prime numbers together (some companies use prime numbers that are hundreds of digits long!), we create an even larger number whose original factors (the two very large prime numbers) are only known to us. We then use this even larger number to encrypt our information.

If anyone else wants to discover what information we are sending, they have to find out what our original factors were. With prime numbers as long as the ones we have used, it could take them years or even decades of constant trial and error before they find even one. This ensures our information is kept safe.

You can find out more about this topic here.

Practice questions

1) A square number and a prime number have a total of 22. What are the two numbers? 

A: 9 and 13

2) Emma thinks of two prime numbers. She adds the two numbers together. Her answer is 36. Write all the possible pairs of prime numbers Emma could be thinking of. 

A: 3 and 33; 5 and 31; 7 and 29; 13 and 23; 17 and 19

3) Circle the two prime numbers – 29, 59, 39, 69, 29

A: 29 and 59

4) Write the three prime numbers which multiply to make 231.

A: 3 x 7 x 11

CHALLENGE QUESTION: Chen chooses a prime number. He multiplies it by 10 and then rounds it to the nearest hundred. His answer is 400. Write all the possible prime numbers Chen could have chosen. 

A: 37, 41 or 43.


Ellie Williams
Ellie Williams
With a love for all things KS2 maths, Ellie is a part of the content team that helps all of the Third Space Learning blogs and resources reach teachers!
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