A little more clarification based on a question someone asked me. If you have upgraded your system to Windows 10, Microsoft registers the components in that system, (something they have been doing since Windows 7), to validate/activate the installation. Once Microsoft has the information you can then wipe the system and install Windows 10 as a bare metal install without needing a serial number or having to reinstall 8.1 first. Microsoft has your system "hardware" registered as being authorized to use Windows 10.
A possibility of this failing to work is if you made substantial changes to the system hardware between doing the wipe and the install.
For those who don't know what Microsoft is looking at, they track the processor, video system, motherboard, network interface and a few other things and create a checksum of sorts based on that information. This will not affect any Surface tablets, only desktop systems.