“What is a prime number?” – it’s one of those maths questions that so many parents are irked by. You’re sitting at the dining table helping child with their homework, but then the topic of prime number comes up. Where do you begin?

To start with, a prime number is a positive integer that is only divisible by 1, and itself. Discover what your child needs to know about prime numbers in KS2 primary school maths.

What are prime numbers?

A prime number is only divisible by 1 and itself. In simple terms, a prime number is a whole number greater than 1 that cannot be divided evenly by any number other than itself, and 1.

This means you cannot divide a prime number by any other whole number without leaving a remainder. For example, 7 is a prime number because it can only be divided by 1 and 7, however 6 is not a prime number because it can be divided by 1, 2, 3 and 6. These are also called the factors of a number, and so prime numbers must only have 2 factors.

What is a whole number? A whole number is any non-negative number without a fractional or decimal part. The whole numbers are {0,1,2,3,4…} and so on.

Is 1 a prime number?

No, 1 is not a prime number and nor is it composite. Many years ago 1 was considered to be prime, and some mathematicians in the 19^th century thought it was. If we look carefully at the definition, a prime number must only be divisible by 1 and itself. The number 1 is divisible by 1 and itself. In this case, 1 is ‘itself.’ We can remove this ambiguity by rewording our definition of a prime number, and say a prime number is any positive number that has exactly 2 factors, itself and 1. If a number has more than 2 factors, then it can not be prime, and we call this number a composite number.

What is a composite number?

A composite number is a whole number that can be written as the product of two smaller numbers. For example, 24 = 6 x 4 and 33 = 11 x 3 show that 24 and 33 are composite numbers. If a number bigger than 1 is not composite, then it is prime, because any prime number cannot be broken down in this way.

Is 2 a prime number? Can prime numbers be even?

Yes. 2 is a prime number. In fact, 2 is the only even prime number. All other even numbers not only have themselves and 1 as factors, but also 2. For this reason, they must be composite. No other even number is prime because it can be expressed as the product of 2 and half of itself. For example, 34 cannot be prime because 34 = 2 x 17. It has four factors: 1, 2, and 17, and 34 (itself). We call 2 an odd prime as it is the only odd number that is considered prime. To conclude, all all even numbers except 2 are composite numbers.

Prime numbers 1-100:

We’ve looked into what it means for a number to be prime, and what makes a number not prime (or composite), but what actually are the prime numbers, and how many prime numbers are there?

Here are the prime numbers between 1-100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

The list stops at 100 but these are not the only primes. It was proved by Greek mathematician Euclid over 2000 years ago that there are in fact unlimited prime numbers. On the other hand, actually calculating them is much, much harder. The largest known prime number was discovered in 2018 and is equal to 2^82,589,933 – 1. This number has approximately 24 million digits, and fortunately you are not expected to know this in KS2 primary school maths. There is actually a $150,000 reward for whoever can find the first prime number with over 100 million digits.

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

Prime numbers are introduced to primary school children for the first time in year 5.

The national curriculum states that a year 5 pupil should:

• Know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers.
• Establish whether a number up to 100 is prime and recall prime numbers up to 19

The non-statutory notes and guidance suggest that in year 5, students understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 9² x 10)

In year 6 primary school maths, pupils will develop their knowledge of primes and according to the national curriculum, should be taught to:

• Identify common factors, common multiples and prime numbers.

Prime numbers up to 19

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

These are the prime numbers that pupils are expected to be able to recall in year 5. Whilst being familiar with these primes is important, here are some useful tricks to identify if a number is prime.

How to identify prime numbers in KS2 Maths

Here is a table of all the numbers between 1 and 100. All of the composite numbers have been crossed off, leaving just the prime numbers. By working through methodically, your child should be able to replicate this table. We actually only need to cross out the multiples of 2, 3, 5, and 7 to find out which ones are prime, and here’s why.

We know from the definition that a prime number is a positive integer only divisible by 1 and itself. That means if we cross out every number from the times tables (not including the 1 times table) then only the prime numbers remain.

Identify the primes – Step 1:

Check for divisibility by 2

We already know that even numbers (apart from 2) cannot be prime because they are all multiples of 2. Start by crossing out every even number. That means any number that ends in 2, 4, 6, 8, or 0 is not prime. By doing this we have also crossed out all the numbers that are also divisible by 4, 6, and 8.

Identify the primes – Step 2:

Check for divisibility by 3

Next we can rule out all the multiples of 3. 3 is prime because the only factors are 1 and itself, 3. However 6 = 2 x 3 and has factors 1, 2, 3 and 6 so it cannot be prime. For the same reason, any other number in the 3 times table will have at least 1, itself and 3 as a factor and so cannot be prime.

To check if a number is divisible by 3, here is very powerful tool…Just add up the digits. If the sum of the digits is a multiple of 3, like 3, 6 or 9 then that number is a multiple of 3 and you can cross it out from the table.

Example 1: Is 168 a multiple of 3?

By adding up the digits, 1 + 6 + 8 = 15 which is a multiple of 3.

We can go 1 step further and add up the digits once more.

1 + 5 = 6 so we have concluded 168 is divisible by 3 and cannot be prime.

Example 2: Is 572 divisible by 3?

5 + 7 + 2 = 14

1 + 4 = 5 which is not a multiple of 3. So 572 is not divisible by 3.

See, easy!

Identify the primes – Step 3:

Check for divisibility by 5:

We don’t need to check for divisibility by 4, or any other even number because we have already crossed off all the multiples of 2. Any number that is a multiple of 4 is also a multiple of 2.

All the multiples of 5 end in either 5 or 0 so we can very quickly rule out anything divisible by 5 (or 10).

Identify the primes – Step 4:

It is not necessary because anything divisible by 6 is divisible by 2, and 3 so we have already eliminated the multiples of 6.

Check for divisibility by 7

This is the trickiest to check for, but through practise and familiarisation with the 7 times table you can work out which numbers are divisible by 7. You can also use long division if you’re not sure.

We don’t need to check for divisibility by 8, 9 or 10 because we have already eliminated all of the numbers divisible by these when we eliminated the multiples of 2 and 3

After following the 4 steps to identify the prime numbers under 100, we have crossed out all of the composite numbers, leaving 25 prime numbers.

When the prime numbers get larger you will need to check for higher factors such at 11, or 13 but in year 5 and year 6 prime numbers will be less than 100 and these 4 steps are sufficient.

Questions

• How many even numbers are prime?
• Is 87 a prime number?
• What are the factors of 12?
• Find the odd one out: 7, 11, 13, 15, 19
• What is the next prime number in the sequence: 2, 3, 5, 7…
• Is 12 composite or prime?
• Why is 2 prime?
• Is 612 divisible by 3

Solutions

• 2 is the only even prime number, so there is only 1.
• No, 87 is a multiple of 3 (using our clever trick, you can spot by counting the digits that 8+7 = 15 and 1 + 5 = 6 which is a multiple of 3 so 87 is divisible by 3 and cannot be prime. Actually 87/3 = 29 and so 87 has factors 1, 3, 29, and 87.
• 1, 2, 3, 4, 6, 12

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

• 15 is the only number that is not prime
• 11
• 12 is composite because it can be written as a product of 2 x 6 or 3 x 4
• 2 is prime because it is only divisible by 1 and itself. This is the definition of a prime number.
• Yes, 612/3 = 204. You can check this by calculating the digit sum like explained in the clever trick. 6 + 1 + 2 = 9 which is a multiple of 3.

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