BLACK for Xbox 360 error

The model numbers need not match. The model you describe will fit an Xbox 360 S (also called "slim", has touch-sensitive drive slot button and "ring of light") or an Xbox 360 E (last generation model, has push-button disc tray) console.

Hey Burns thanks for keeping us in the loop!

We suggest looking into our Add or remove an Xbox 360 Hard Drive page since we have some very helpful information regarding the Hard drive.
Now if a new hard drive is what you're looking for we suggest looking into our
Where to Buy page since it addresses all our recommended retailers. Give these a look over and let us know if we can further assist in this or any other issue or inquiry!

That game is definitely backwards compatible, but in order to run backwards compatible games on the 360 it requires an official MS hard drive. If you don't have a hard drive for your console, you would need one.

Thank you all for your advice and helping me to resolve this simple issue. This is the result I was looking for.

The hard drive in question is the one that most likely is already in your Xbox 360 console. The key is that it must be one produced by Microsoft; third-party drives that still fit Xbox 360 won't have the partition that has the needed emulation files.

That said, Xbox 360 has been out of production for 2 1/2 years now, so replacement parts (such as said official hard drives) may be harder to come by as time goes on. The Xbox One doesn't need anything more than what it already has, since the file that will
install on your console for "Black" will already have everything it needs to run properly. So if you've already been considering an upgrade, this might be the time, especially with holiday pricing specials on new Xbox One consoles.

Incidentally, on Xbox One, the game can be installed on either the console's built-in hard drive or any compatible external hard drive that is connected to it.