I don't know the number off hand, but you can call Apple or go into the Apple store and do it there. It may also be possible to do online. I believe there is some remote diagnostic test they run on it then you pay the money and you're all set.
1. Sign into your Apple Support Site --> https://support.apple.com/my-support
2. Locate the Apple Watch then select Add Coverage for Apple Care +
3. Enter phone # or email address
4. Apple will send you a link to the one you entered
5. Click link and let it run the diagnostics
6. Once done, the Apple page will refresh and you can buy Apple Care +