How to make multiple circles into a single shape so that I can fill the overlapping area

I'm trying to learn illustrator.

I've drawn this alarm clock, using overlapping circle shapes. Now I'm trying to figure out how to fill the rim and frame of the clock the same colour as the bells and the feet, and then I want to fill the face of the clock with a separate fill layer. How can I achieve this? I have tried every tool in the Path menu and none of them do this job.

Thank you