Prime & Composite Numbers
Learn to identify prime and composite numbers, understand factors, and break numbers down using prime factorisation.
What Are Prime Numbers?
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. It cannot be divided evenly by any other number.
Prime Numbers up to 50
Remember: 1 is NOT a prime number because it only has one factor (itself). Also, 2 is the only even prime number!
What Are Composite Numbers?
A composite number is a whole number greater than 1 that has more than two factors. It can be divided evenly by at least one other number besides 1 and itself.
Example: 12
Factors of 12: 1, 2, 3, 4, 6, 12
12 has 6 factors, so it is composite.
Example: 7
Factors of 7: 1, 7
7 has exactly 2 factors, so it is prime.
How to Test if a Number Is Prime
To check whether a number is prime, try dividing it by every prime number up to its square root. If none divide evenly, the number is prime.
Quick Tests
- Divisible by 2? — Even numbers (except 2) are composite.
- Divisible by 3? — Add the digits. If the total divides by 3, so does the number.
- Divisible by 5? — Numbers ending in 0 or 5 are divisible by 5.
- Divisible by 7, 11...? — Try dividing and see if there is a remainder.
Prime Factorisation
Prime factorisation means breaking a composite number down into a product of prime numbers. Every composite number can be written as a unique product of primes.
Factor Tree for 36
36
/ \
2 18
/ \
2 9
/ \
3 3
36 = 2 × 2 × 3 × 3
Key Vocabulary
Prime Number
A number greater than 1 with exactly two factors: 1 and itself.
Composite Number
A number greater than 1 that has more than two factors.
Factor
A number that divides evenly into another number with no remainder.
Prime Factorisation
Writing a number as a product of its prime factors (e.g. 12 = 2 × 2 × 3).
Worked Examples
Is 29 prime or composite?
Step 1: Check divisibility by 2 — 29 is odd, so no.
Step 2: Check divisibility by 3 — 2 + 9 = 11, not divisible by 3.
Step 3: Check divisibility by 5 — does not end in 0 or 5.
Answer: 29 is prime (only factors are 1 and 29).
Find the prime factorisation of 60.
Step 1: 60 ÷ 2 = 30
Step 2: 30 ÷ 2 = 15
Step 3: 15 ÷ 3 = 5
Step 4: 5 is prime, so stop.
Answer: 60 = 2 × 2 × 3 × 5
List all the factors of 24 and decide: prime or composite?
Step 1: Factor pairs: 1 × 24, 2 × 12, 3 × 8, 4 × 6
Step 2: Factors: 1, 2, 3, 4, 6, 8, 12, 24 (8 factors)
Answer: 24 is composite because it has more than two factors.
Knowledge Check
Select the correct answer for each question. Click “Check Answer” to see if you are right.
Question 1
Which of these numbers is prime?
Question 2
What is the prime factorisation of 18?
Question 3
How many prime numbers are there between 10 and 20?
Question 4
Which statement about the number 1 is correct?
Question 5
What is the prime factorisation of 42?
Key Concepts Summary
- ●A prime number has exactly two factors: 1 and itself.
- ●A composite number has more than two factors.
- ●The number 1 is neither prime nor composite.
- ●Prime factorisation breaks a number into a product of primes using a factor tree.
- ●2 is the only even prime number.