How to teach prime and composite numbers

Grade 4 to Grade 6

A prime number has exactly two factors, 1 and itself, so it cannot be split into smaller equal groups larger than one. A composite number has more than two factors. The number 1 is neither, because it has only one factor. Primes are the building blocks of every other number, which is why factors need to be secure first.

How to teach it

1. Build on factors: a number is prime if the only rectangle you can make from its counters is a single row (7 counters only make 1 x 7).
2. List the factors of a number in pairs and count them: exactly two means prime, more than two means composite.
3. Learn the primes to 20 by heart (2, 3, 5, 7, 11, 13, 17, 19) and use the Sieve of Eratosthenes on a hundred square to find the rest.
4. Stress the two special cases: 2 is the only even prime, and 1 is neither prime nor composite.
5. Practise sorting numbers into prime and composite, explaining the factor count each time.

Common mistakes

• Calling 1 a prime number (it has only one factor, so it is neither).
• Assuming every odd number is prime (9, 15 and 21 are composite).
• Forgetting that 2 is prime because it is even.
• Deciding a number is prime without actually checking all its factors.