I want to complete a factory reset on my 2011 MacBook Pro

How you do it depends on what OS is currently installed.

Try downloading the macOS 10.13 High Sierra installer (the latest version compatible with your Mac) using the links in this Apple article:

https://support.apple.com/en-us/HT201372

I recommend creating a bootable macOS USB installer so you have more options in case something goes wrong.

If you are already running macOS 10.12.6 or 10.13, then you can access the online macOS installer by booting into Internet Recovery Mode using Command + Option + R.

To perform a clean install you first need to erase the whole physical drive:

https://support.apple.com/guide/disk-utility/erase-and-reformat-a-storage-device-dskutl14079/mac

Make sure to have a good backup before performing a clean install.

not much to do other than:

save all your personal data

erase the drive but I'd swap in a SSD

clean the inside while you are at it

install a compatible operating system