Factors, Multiples and Primes
Factors, multiples and prime numbers are important number skills in GCSE Maths. They are used in fractions, ratio, algebra, HCF, LCM and problem solving questions.
Factor: divides exactly into a number.
Multiple: appears in a times table.
Prime number: has exactly two factors.
Factors
A factor of a number divides into it exactly with no remainder.
Example 1: Find factors
Find the factors of 18.
Check the factor pairs:
1 × 18, 2 × 9, 3 × 6
The factors of 18 are 1, 2, 3, 6, 9 and 18.
Multiples
A multiple is the result of multiplying a number by an integer.
Example 2: Find multiples
Write the first five multiples of 7.
7, 14, 21, 28, 35
Prime numbers
A prime number has exactly two factors: 1 and itself. The number 1 is not prime because it has only one factor.
First few prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Example 3: Is 29 prime?
The number 29 has only two factors: 1 and 29.
So 29 is prime.
Highest common factor
The highest common factor, or HCF, is the biggest number that divides exactly into two or more numbers.
Example 4: Find the HCF
Find the HCF of 24 and 36.
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
The highest common factor is 12.
Lowest common multiple
The lowest common multiple, or LCM, is the smallest number that is a multiple of two or more numbers.
Example 5: Find the LCM
Find the LCM of 6 and 8.
Multiples of 6:
6, 12, 18, 24, 30
Multiples of 8:
8, 16, 24, 32
The lowest common multiple is 24.
Prime factorisation
Prime factorisation means writing a number as a product of prime numbers.
Example 6: Prime factorisation of 60
Break 60 down into prime factors:
60 = 2 × 30
30 = 2 × 15
15 = 3 × 5
60 = 2² × 3 × 5
A common mistake is saying that 1 is prime. It is not prime because it only has one factor.
HCF questions usually involve sharing or grouping. LCM questions often involve repeated events happening at the same time again.
Video explanation
A short Worthing Maths Tutor video explanation for factors multiples and primes can be embedded here later to improve student engagement and time on page.
Practice questions
- List all the factors of 20.
- Write the first five multiples of 9.
- Is 31 prime?
- Find the HCF of 18 and 30.
- Find the LCM of 4 and 10.
Answers
- 1, 2, 4, 5, 10, 20
- 9, 18, 27, 36, 45
- Yes
- 6
- 20
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