And one way to really internalize this is to start taking square roots (in your head, of course) of large numbers you see around you. Maybe license plate numbe

And one way to really internalize this is to start taking square roots (in your head, of course) of large numbers you see around you. Maybe license plate numbers if you're waiting in traffic. If you have extra time, you can do one step of refinement of your original guess, as done in the OP. ("Take the residual R, and the guessed-at factor p, and find the largest number N such that 2 * p * N <= R")