31 March 2024

The Factor Method for HCF and LCM

I've blogged and presented about methods for finding a Highest Common Factor and Lowest Common Multiple numerous times, but I still think that The Factor Method* deserves a bit more love. 

[*also known as The Ladder Method, and various other names]

When I trained to be a teacher I was told that the Venn Method was THE way to find HCFs and LCMs. A few years later a colleague showed me a very different method that she'd learnt from a student, and this is what started my fascination with methods. I went on to write the book A Compendium of Mathematical Methods

Never trust anyone who says that a particular method is the best way of doing something because there is absolutely no research to back up their claim (it's a great shame that no one in maths education academia does large scale studies comparing methods - it seems like a big gap in our profession's pedagogical subject knowledge). However, I think it's reasonable to describe something as a favourite method. The Factor Method is definitely my favourite.

I've a made a 28 minute video explaining in detail how to find HCFs and LCMs using the Factor Method. This is a video for teachers, not for students. In it I model a number of examples, including those that might spark discussion. I also talk about how we can use this method to find an HCF and LCM of three numbers, and how we can easily use the Factor Method to work backwards.

I'm not a YouTuber so please forgive the ropey handwriting...


  1. Excellent. I agree that the proper term is favourite and not best.

  2. Great to see a this new method, thank you, I love it. I agree, there is never one best method, it all depends on the individual students. Although teaching experience will often give us a ‘favourite’ method.

  3. This is great - especially how you chose very important types of questions to see how the method presents across different skills. Thank you for this

  4. As you stated, it is important that we acknowledge that there are different methods and that students understand they come with different pros and cons. I like the efficiency of this method.