The last three numbers of the N-reg is the ship number of the aircraft in question. For example, N173461 is ship number 461.
It also helps CO crews tell the difference between the 733, 735, 73G, and 738. 733 have ship numbers 3XX. 735 have 6XX. 73G have 7XX. 738 have 2XX.
To me this seems like a more logical system than N242UA, N244UA, etc because it keeps the N-reg and ship number as one single number. Delta's newest 777-232 is N863DA but is ship number 7004 in the fleet. Although the registrations are not pretty looking, they do serve a logical purpose.
Hope this helps.