Finding "a choose b" Numbers: A Quick Guide

[Dragonfall]

Is there a fast way of determining whether a number x is of the form "a choose b" for some a and b (a and b are not given, obviously)? I guess a good way to start is to find the largest factorial which divides x.

 

[qntty]

Every natural number has that property, remember that x choose 1 is x.