What is a prime number?
Year 5 introduces prime numbers, prime factors and composite numbers. Year 6 identifies them alongside common factors and common multiples. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
A prime number is a whole number with exactly two factors: 1 and itself.
What it means
7 is prime, because the only way to make 7 by multiplying two whole numbers is 1 × 7. 8 is not prime, because 2 × 4 = 8 as well.
A whole number bigger than 1 that is not prime is called a composite number. 1 is not prime and not composite: it has only one factor.
The prime numbers under 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. There are 25 prime numbers under 100.
A worked example
Is 51 a prime number?
- Try dividing by the small primes. 51 is odd, so 2 does not go in.
- The digits add up to 5 + 1 = 6, which is in the 3 times table, so 3 goes in: 51 ÷ 3 = 17.
- 51 = 3 × 17, so it has four factors (1, 3, 17 and 51). 51 is not prime.
The common mistake
Thinking every odd number is prime. 9, 15, 21, 25, 27 and 51 are all odd, and none of them is prime. And 2 is prime even though it is even: it is the only even prime.
How it comes up in the 11+
Which of these numbers is prime: 21, 27, 29, 33, 39?
Answer: 29
- 21 = 3 × 7
- 27 = 3 × 9
- 33 = 3 × 11
- 39 = 3 × 13
- 29 has no factors other than 1 and 29, so 29 is the prime number.
Related words and practice
More maths words
Questions parents ask
Is 1 a prime number?
No. A prime number has exactly two factors, and 1 has only one: itself.
Is 2 a prime number?
Yes. Its only factors are 1 and 2. It is the only even prime number, because every other even number can be divided by 2.
How many prime numbers are there under 100?
There are 25 prime numbers under 100. The last one is 97.
Knowing the words is half of an 11+ maths question
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