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Prime Numbers
Year 8 • Number
Lesson: Prime Numbers
Understand prime and composite numbers, learn how to test if a number is prime, and practise with exam-style questions – perfect for Year 8 students.
Lesson Objectives
- Understand what prime numbers and composite numbers are.
- Identify prime numbers up to at least 50.
- Use divisibility tests to check if a number is prime.
- Write numbers as products of prime factors.
1. What Are Prime Numbers?
A prime number is a whole number greater than 1 that has exactly two different factors:
1 and itself.
Examples of prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 …
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 …
Check 7: Factors of 7 are 1 and 7 → only two factors → 7 is prime.
2. Composite Numbers and Special Cases
A composite number is a whole number greater than 1 that has more than two factors.
Composite Numbers
4 → factors: 1, 2, 4
6 → factors: 1, 2, 3, 6
9 → factors: 1, 3, 9
12 → factors: 1, 2, 3, 4, 6, 12
4 → factors: 1, 2, 4
6 → factors: 1, 2, 3, 6
9 → factors: 1, 3, 9
12 → factors: 1, 2, 3, 4, 6, 12
Special Cases
1 is not prime and not composite.
0 is not prime or composite.
2 is the only even prime number.
1 is not prime and not composite.
0 is not prime or composite.
2 is the only even prime number.
3. How to Check if a Number is Prime
To test if a number is prime, check whether it is divisible by any smaller prime numbers.
Steps to check if a number is prime:
- If the number is even and greater than 2 → it is not prime.
- Check divisibility by 3, 5, 7, 11, … up to about the square root of the number.
- If no smaller prime divides it exactly → the number is prime.
Example:
Is 29 a prime number?
- 29 is not even → not divisible by 2.
- 2 + 9 = 11 → not a multiple of 3 → not divisible by 3.
- 29 ÷ 5 is not a whole number.
- 29 ÷ 7 is not a whole number.
No smaller prime divides 29 → 29 is prime.
4. Prime Numbers up to 50
It is useful to memorise the prime numbers up to 50:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
5. Prime Factorization
Any composite number can be written as a product of prime factors.
This is called its prime factorization.
Examples:
12 = 2 × 2 × 3 = 2² × 3
18 = 2 × 3 × 3 = 2 × 3²
30 = 2 × 3 × 5
12 = 2 × 2 × 3 = 2² × 3
18 = 2 × 3 × 3 = 2 × 3²
30 = 2 × 3 × 5
Practice Questions
A. Prime or Composite?
State whether each number is prime or composite:
- 2
- 9
- 11
- 21
- 37
B. Circle the Prime Numbers
From the list below, identify all prime numbers:
4, 5, 7, 9, 10, 13, 15, 17, 19, 21, 23, 25
C. Prime Factorization
Write each number as a product of prime factors:
- 12
- 18
- 24
- 40
D. Check if the Number is Prime
Using divisibility tests, decide if each number is prime:
- 29
- 39
- 41
- 51
E. Word Problems
-
A teacher wants to arrange 23 chairs in equal rows with no chair left over.
In how many different ways can she arrange the rows? What does this tell you about 23? -
A number of sweets can be shared equally among 2, 3, 4, 5 and 6 children, but not among 7 children.
Is this number more likely to be prime or composite? Explain why.
✅ Show Answer Key
A. Prime or Composite?
- 2 → Prime (factors: 1, 2)
- 9 → Composite (factors: 1, 3, 9)
- 11 → Prime (factors: 1, 11)
- 21 → Composite (factors: 1, 3, 7, 21)
- 37 → Prime (factors: 1, 37)
B. Circle the Prime Numbers
Prime numbers: 5, 7, 13, 17, 19, 23
C. Prime Factorization
- 12 = 2 × 2 × 3 = 2² × 3
- 18 = 2 × 3 × 3 = 2 × 3²
- 24 = 2 × 2 × 2 × 3 = 2³ × 3
- 40 = 2 × 2 × 2 × 5 = 2³ × 5
D. Check if the Number is Prime
- 29 → Prime (not divisible by 2, 3, 5)
- 39 → Composite (39 = 3 × 13)
- 41 → Prime (no smaller prime divides it)
- 51 → Composite (51 = 3 × 17)
E. Word Problems
-
23 can only be arranged as 1 row of 23 or 23 rows of 1 → only two factors (1 and 23).
So 23 is a prime number. -
The number can be divided equally by 2, 3, 4, 5 and 6 → it has many factors → it is
composite, not prime.
© Aviate Learning – Prime Numbers (Year 8)