That arrangement changed a number of years ago. For a while keys were embedded in hardware and now Windows 10 just fingerprints your hardware so it can restore your license from bare hardware. If you are prompted for a key during Windows install you just click the link at the bottom of the screen saying you don't have a key and Windows will reactivate once connected to the Internet after the installation. An important point is that it must be the same version of Windows, so if you had a Home version you may not activate a Pro or Enterprise version of Windows.
I should also point out that your machine has a restore partition by default. If you wipe the drive and install clean you will no longer have it. I personally prefer this and would never go back to a factory configuration on any notebook, but if that's something you want then one way to achieve that would be to take out the boot drive and replace it with a new one before the clean install. Keep the old one in a box for a rainy day.
To answer your original question, Windows 10 makes things pretty easy. Just click Start and begin typing "reset this pc". Windows 10 reset has a few options from one that preserves data to one that wipes everything.
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