Highest Common Factor
The highest common factor of two numbers is the largest number that divides both of them exactly.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
The highest common factor of two numbers is the largest number that divides both of them exactly.
- List or factorise both numbers
- Take the prime factors they share
- HCF of 12 and 18 is 6
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Highest Common Factor?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Highest Common Factor. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Highest Common Factor in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Highest Common Factor gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Highest Common Factor in detail
The highest common factor (HCF) of two or more numbers is the largest number that divides all of them exactly. For 24 and 36 the common factors are 1, 2, 3, 4, 6 and 12, so the HCF is 12. You can find it by listing factors or by taking the shared primes from each prime factorisation.
The HCF is used to simplify fractions to their lowest terms, to split quantities into the largest equal groups and to factorise expressions by taking out the biggest common term. For example, 24 sweets and 36 stickers can be shared among at most 12 identical party bags.
How the interactive helps you understand Highest Common Factor
Watch the Venn diagram in the interactive. Use any sliders or buttons it offers to change the values and see how the Venn diagram responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Highest Common Factor.
Real-life uses and examples
- Check a homework answer about Highest Common Factor by estimating first, then working it out step by step.
- Use Highest Common Factor when comparing prices, discounts or recipe quantities in everyday life.
- Explain Highest Common Factor to a friend with a simple picture, such as a row of tiles or a bag of sweets.
Common mistakes to avoid
- Memorising the steps for Highest Common Factor without checking why they work.
- Forgetting units, signs or brackets when you apply Highest Common Factor.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Highest Common Factor
What is Highest Common Factor?
The highest common factor of two numbers is the largest number that divides both of them exactly.
What are the most important points about Highest Common Factor?
The main points are: List or factorise both numbers; Take the prime factors they share; HCF of 12 and 18 is 6.
Why is Highest Common Factor useful?
Understanding Highest Common Factor gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Highest Common Factor?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Highest Common Factor?
Related topics in Mathematics include Order of Operations, Equivalent Fractions, Mixed Numbers and Improper Fractions.