How do I find the highest common factor of two numbers?

The factors of a number are all the numbers that divide into it, so the HCF of two numbers is the highest number that is a factor of both numbers. I'd work it out by create a list of all of the prime factors of the two numbers, which you could find using a tree (like this: use whiteboard). Find all of the common factors, i.e. the numbers which are in both lists. If you multiply all the common factors, you will have the highest common factor. 

As an example, the prime factors of 72 are 2, 2, 2, 3, 3 and the prime factors of 84 are 2, 2, 3, and 7. The common factors are 2, 2, and 3. 2 x 2 x 3 = 12. The highest common factor of 72 and 84 is therefore 12.