Hi math forum folks!

I'm trying to understand sigma functions in the context of a homework question that I have. I attached an image of the question in this post. The issue that I'm facing with12cis that I got the wrong answer. To my understanding f(12) does not equal f(3) x f(4) - which is contrary to the textbook answer. I would like some clarification on why they equal each other (or if the textbook is wrong).

Additionally, I would like to understand12d.better. The textbook said that two sigma functions would equal another "whenever a and b have no common factors other than 1", which I don't really understand why this would be the case.

I hope that someone can help me out!!!

- Olivia