Factors, Multiples, Primes, HCF and LCM

This lesson covers key topics from the AQA GCSE Mathematics Number specification: identifying factors, multiples, and prime numbers, and using prime factorisation to find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM). These concepts are tested regularly on both papers and form the building blocks for work with fractions, algebra and more.

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Factors

A factor of a number is any whole number that divides into it exactly, leaving no remainder.

Finding Factors

To find all the factors of a number, work through pairs systematically starting from 1.

Worked Example: Find all the factors of 36.

Pair	Calculation
1 x 36	1 and 36 are factors
2 x 18	2 and 18 are factors
3 x 12	3 and 12 are factors
4 x 9	4 and 9 are factors
6 x 6	6 is a factor (pair repeats)

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36