Factors, Multiples, HCF and LCM

Factors, Multiples, HCF and LCM

Factors divide a number exactly; multiples are the results of multiplying a number by whole numbers. Prime factorisation helps organise them. The highest common factor (HCF) is the largest factor shared by two numbers. The lowest common multiple (LCM) is the first positive multiple shared by two numbers; it helps with common denominators and repeated schedules.

Worked example

Factors of 12 are 1, 2, 3, 4, 6 and 12. Factors of 18 are 1, 2, 3, 6, 9 and 18, so their HCF is 6. Multiples of 4 and 6 first meet at 12, so LCM is 12.

Exam method

1. Decide whether the question asks for a factor or multiple. 2. List systematically or use prime factors. 3. Choose the greatest shared factor or lowest shared multiple as required.