A prime number has exactly two factors: 1 and itself, like 2, 3, 5, 7 and 11. A composite number has more than two factors, like 12. The number 1 is neither, because it has only one factor. 2 is the only even prime. Being odd does not make a number prime: 91 = 7 × 13. To test a number, try dividing by 2, 3, 5 and 7.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- prime number
- a number with exactly two factors, 1 and itself
- composite number
- a number with more than two factors
Worked examples
Which of these numbers is prime? 1, 15, 17, 51
- 1.1 has only one factor. 15 = 3 × 5 and 51 = 3 × 17.
- 2.17 has only the factors 1 and 17.
= 17
Is 91 a prime number or a composite number?
- 1.Try 2, 3, 5 and 7.
- 2.91 = 7 × 13, so it has more than two factors.
= composite
How many prime numbers are there between 20 and 40?
- 1.Test the odd numbers: 21, 25, 27, 33, 35 and 39 all have other factors.
- 2.23, 29, 31 and 37 are prime.
= 4
For parents
Method: Count the factors
What to say: Can you find a factor other than 1 and the number itself?
Common mistakes:
- Thinks 1 is a prime number.
- Thinks every odd number is prime.
- Only checks small factors like 2, 3 and 5, so thinks numbers like 49, 51 or 91 are prime.
- Thinks 2 cannot be prime because it is even.
- Knows the factors but mixes up the words 'prime' and 'composite'.
- Thinks any odd number not ending in 5 is prime, judging by the last digit.