Imagine a science experiment involving 500 light bulbs, each numbered from 1 to 500, and all initially switched on. A scientist introduces a process where, for every natural number 'n' from 1 to 500, he toggles (switches the state) of all light bulbs whose numbers are divisible by 'n'. So, during the first pass, every bulb is toggled since 1 is a factor of all numbers. During the second pass, the scientist toggles every second bulb (those with numbers that are multiples of 2), and so on, until he reaches the 500th pass.

The question is: after going through this entire process, how many of the 500 light bulbs will remain illuminated?