If I factory reset my computer will I have to enter a windows key or put in the windows disc because I have neither?

You may have the Windows "D" partition which is the Windows Recovery partition that contains the Windows operating system copy that is used to recover your operating system after a catastrophic failure of your computer. Just make sure you have all personal files backed up because your computer system will look the same as when it was new. You can also download the free software Belarc Advisor to get all product keys of the Microsoft software installed on your computer.

Unless it has a recovery partition which is undamaged you will need a disk.

Usually there is no need for a disk because of the hidden windows partition the product key is automatically entered unless the partition is corrupt

I had to put the disk in when I did that.

You could install Ubuntu, that is free and it's just like Windows if you can't afford to buy a windows disk

You could download and install a Linux operating system.