If I factory reset my computer, will I have to put in a windows key or disc?

Maybe. Depends on the factory...

AFAIK, there is no factory reset in computers.

Windows disc

No a factory reset is your Windows disk and key! It copy's it to the drive erasing whatever mess is fouling you computer thus making it run like new!

Before you do it save your files on a thumb drive.

No

You won't need a key or disc.