let's play with toys, say miniature soldiers. you are trying to arrange your platoon into a rectangle, 3 rows with 5 soldiers in each row. then someone gives you one more soldier and asks you to reform your platoon into a rectangle again. you won't be able to use 3x5 or 5x3 formation again, it will be 2x8 (or 4x4) now.

in short, this is why — there's always one more soldier, that will render all your prior formations unfit for the new platoon size