Do companies have a way to identify a computer right down to the exact computer you are signing in from?

Whenever I try to log into my chase account, I get an error message saying something like " we don't recognize the device you are signing in from" Then I have to go though a host of security questions and get the code text sent to me.

Its very annoying to do this everything especially when I am typing in the correct user name and password from the same computer.

I thought they could only get information such as Web browser used(Internet explorer, firefox, chrome,etc..), maybe operating system, IP address, and cookies stored on the web browser,etc..

Do company really have a way to recognize a computer down to an exact computer used when signing into their website?

Thanks.