If you managed to use the product key you could use cmd prompt (as Administrator):
wmic path softwareLicensingService get OA3xOriginalProductKey
If you have scratched the key off to the point that it is unreadable, you might be out of luck and need to purchase a new product key.
Edit: If you recently purchased the device from a vendor, you may be able to contact them to see if that information is on file.
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