Sheet № 132 · Foundation + Higher · AQA · Edexcel · OCR
Factors, Multiples and Primes –
Factors, multiples, and primes form the foundation of number work at GCSE. These concepts appear directly on exam papers and also underpin topics such as HCF, LCM, fractions, and algebra.
§Key definitions
Question:
List all the factors of 36.
Answer:
1, 2, 3, 4, 6, 9, 12, 18, 36
Q1 (Foundation):
List all the factor pairs of 48.
Q2 (Foundation):
Write down the first six multiples of 9.
Q3 (Higher):
Write 504 as a product of its prime factors in index notation.
§Formulas to memorise
Product of primes: write a number using only prime factors with index notation, e.g. 60 = 2² × 3 × 5
A number is prime if it has exactly two factors: 1 and itself
Worked example
List all the factors of 36.
Working:
⚠ Common mistakes
- ✗Thinking 1 is a prime number. It is not — a prime must have exactly two distinct factors, and 1 only has one factor.
- ✗Missing factor pairs. Work systematically from 1 upwards to ensure you find every pair. Stop when the factors start repeating.
- ✗Not fully breaking down the factor tree. Every branch must end at a prime. If you stop at 4, 6, 9, or any composite number, the factorisation is incomplete.
✦ Exam tips
- →Memorise the prime numbers up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
- →Use divisibility rules: a number is divisible by 3 if its digit sum is divisible by 3.
- →Always present your final answer in index notation — examiners expect this.