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
- 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).
- List the factors of a number in pairs and count them: exactly two means prime, more than two means composite.
- 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.
- Stress the two special cases: 2 is the only even prime, and 1 is neither prime nor composite.
- 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.
Frequently asked questions
What is the difference between a prime and a composite number?
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.
What age or grade are prime and composite numbers taught?
Prime and composite numbers are usually taught from Grade 4 to Grade 6, once factors are secure. Students learn the primes to 20, use the factor count to classify numbers, and often meet the Sieve of Eratosthenes for finding primes.
Is 1 a prime number?
No. The number 1 is neither prime nor composite, because it has only one factor, itself. A prime needs exactly two different factors, 1 and the number, and 1 does not meet that condition. Calling 1 prime is a very common mistake.
Is 2 a prime number?
Yes. 2 is prime because its only factors are 1 and 2. It is also the only even prime number, since every other even number has 2 as an extra factor and is therefore composite. Students often wrongly assume all primes must be odd.
What are the prime numbers up to 20?
The primes up to 20 are 2, 3, 5, 7, 11, 13, 17 and 19. Learning these by heart is a useful foundation, and the Sieve of Eratosthenes on a hundred square is a reliable way to find the rest.
What is the Sieve of Eratosthenes?
It is a method for finding primes on a hundred square. You keep 2 and cross out its multiples, keep 3 and cross out its multiples, and continue. The numbers left uncrossed are the primes, because they have no factors other than 1 and themselves.
Are all odd numbers prime?
No. Many odd numbers are composite, such as 9, 15 and 21, which each have factors beyond 1 and themselves. Being odd only means not divisible by 2; a number is prime only if it has exactly two factors, so odd numbers must still be checked.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.