The serial number is not a product serial. It is a 12 digit code that you receive after registering personal details such as name and email when downloading the RealSense SDK. You do not need a serial number before you download.
If you mean the serial number that your colleague had, you shouldn't need it. If you register your details on the registration site then you should get your own unique serial. The serial does not link to the camera hardware. It's just a way of storing in your registered Intel online account what programs you are using.
OK. I figured out how to get the serial number and download the SDK. I'm going to include screenshots since this is not intuitive at all.
1. Go to: Intel® RealSense™ SDK | Intel® Software
2. DO NOT CLICK ON FREE DOWNLOAD!
3. Scroll down and click on Download under SDK Components Download -> Essentials
Then it will take you to this page where it gives you a serial number and an actual download button:
Once that is done you can also download this software from https://registrationcenter.intel.com/en/products/
Man, Intel does not make this easy! Good luck!