ARM Processor: Checking validity of immediate value (Bit rotation)

Question

In an ARM Processor with 32-bit instruction size, I understand that ARM can use 8-bit to store the value and 4-bits for bit rotation instructions (bit-shift the 8-bit value by multiples of 2) in order to gain a much better range than just simple 8/12-bit representation for immediate values.

While I understand the process of how ARM can get the extended range, I am interested to know if there is a way to easily check if our chosen immediate value is valid under this scheme. What kind of characteristics of the number (be it in binary or hex) are we looking out for that can help us determine if this value is valid under ARM's bit-rotation scheme?

Edit: Here is a link to the concept I am talking about.