N3NumberFoundation

Factors, Multiples & Primes

Factors, multiples and prime numbers describe how numbers are built from each other. They lead to two key exam skills: finding the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM).

35 min Video by Maths Genie AQA GCSE Maths

Factors, Multiples and PrimesWatch the walkthrough, then read the notes below.

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What you'll learn

Find the factors and multiples of a number
Identify prime numbers
Write a number as a product of prime factors
Find the HCF and LCM of two numbers

The key words

A $factor$ divides exactly into a number (factors of 12: 1, 2, 3, 4, 6, 12). A $multiple$ is in that number’s times table (multiples of 4: 4, 8, 12, …). A $prime$ number has exactly two factors: 1 and itself (2, 3, 5, 7, 11, …).

Tip — 1 is NOT prime (it has only one factor). 2 is the only even prime.

Prime factors, HCF and LCM

Every number can be written as a product of primes using a factor tree, e.g. $12 = 2^{2} \times 3$ . From the prime factors you can find the HCF (multiply the primes they share) and the LCM (multiply each prime the most times it appears in either number).

12 = 2^{2} \times 3

18 = 2 \times 3^{2}

2HCF = shared primes =

2 \times 3 = 6

3LCM =

2^{2} \times 3^{2} = 36

AnswerHCF

= 6

, LCM

= 36

Remember these

12 = 2^{2} \times 3

Product of prime factors (from a factor tree).

HCF \times LCM = a \times b

A handy check for two numbers a and b.

Watch out for these

Saying 1 is a prime number.

A prime has exactly two factors; 1 has only one, so it is not prime.

Mixing up HCF and LCM.

HCF is the biggest number that divides both (smaller); LCM is the first number both go into (larger).

Key takeaways

Factors divide in; multiples are in the times table.
Primes have exactly two factors; 1 is not prime.
Use prime factors to find HCF (shared) and LCM (all, most times).

Test yourself

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