Euclid’s Algorithm (EA) is a simple process by which you can find out the greatest common factor (GCF) of two numbers by repeatedly subtracting the smaller number from the bigger one. Euclid proved and used it in his series of textbooks, called the ‘Elements’.
On my first practicum, I was distraught to find that when I was teaching factorisation by common factor to my year 10s, many of them couldn’t remember their times tables. I couldn’t find any method of getting them to find the GCF between two numbers, besides by saying ‘can the two numbers be divided by two? Ok, factorise out that two. Can it still be factorised by two? Ok, how about 3? How about 5?’, and slowly factorising each prime factor one at a time. It wasn’t until after the practicum I stumbled across EA, and felt incredibly frustrated, as if only I knew it before, so that I could teach the students a new way to find the GCF. After all, why insist on a method that they have never mastered, as they’re unlikely to master it if the 11 teachers before me have failed.
This algorithm (and booklet) can be used for factorising by common factor, for harder, real-world worded optimisation problems. It can even derive the golden ratio.
For the booklet to print properly and to work as a booklet, it needs to be printed double sided, flipped on the short side of the page.