What is a Factor?
Before we can find the highest common factor, we need to make sure we understand what a factor is.
A factor is a number that divides exactly into another number, leaving no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 exactly.
To find all the factors of a number, think about every pair of numbers that multiply together to give that number. These are called factor pairs.
Finding all factors of 24
We look for factor pairs:
So the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
Tip: Always list factors in order from smallest to largest so you don't miss any!
To make sure you have found all the factor pairs, start at 1 and work upwards. Stop when the two numbers in a pair meet or cross over. For 24, once you reach 4 × 6, the next pair would be 6 × 4, which you already have!
What is the Highest Common Factor (HCF)?
The Highest Common Factor (HCF) of two or more numbers is the largest number that divides exactly into all of them. It is sometimes called the Greatest Common Factor (GCF).
The word "common" means shared — we are looking for factors that appear in the lists of both numbers. The word "highest" means we want the biggest one.
Imagine you have 18 apples and 24 oranges. You want to arrange them into equal groups — each group must have the same number of apples and the same number of oranges, with nothing left over. The largest group size that works for both is the HCF! Since HCF(18, 24) = 6, the largest equal group size is 6 — giving you 3 groups of apples and 4 groups of oranges.
The HCF will always be less than or equal to the smaller of the two numbers. It can never be larger than either number!
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