What is the greatest common factor? How do you know when you have found the greatest one?

The greatest common factor is the term that factors out of all elements of a polynomial. The greatest common factor can be found by factoring each individual term of a polynomial. This can be a tedious process and it is often best to analyze each term of a polynomial before going through with all of that. Often times it can be easiest to identify the greatest common factor by finding out how each term is related. I will show you how to find the greatest common factor of the polynomial. 10x^2y^2+ 5xy+20y. In this equation the highest common factor is 5. You must now identify the highest common variable between all elements of the polynomial. In this equation the highest common factor is just y so our new greatest common factor is 5y. When we factor this out of our polynomial we get 5y(2x^2y + x + 4x).