I have been using this method for 2 years now! you can do it for GCF too, but a bit different for the last step! Finding the least (lowest) common multiple (LCM) using the upside down birthday cake method
Ramblings of a fifth and sixth grade teacher.: Common Core Math Training Using a Venn diagram to teach GCF is a great way to visually see the results. It's a good tool especially for visual learners.