Shawnbob's Gravitational Factorizer

We all learn to factor numbers in school. 6 = 3*2 49 = 7*7 etc.

well what happens if you don't know the exact number you start with but you just wanna factor it anyway (for fun I suppose)? I.E. you wanna factor some number of things without counting them first. Assuming you just start with a generic pile.

I'll use marbles as an example. Imagine two parallel plates of glass exactly one marble thickness apart. Then imagine two vertical sidewalls between the plates and one is moveable but stays vertical. So you dump an uncounted number of marbles in between the plates and just start moving the sidewall out until the surface of marbles is a straight line. You end up with a rectangle of factored marbles (x columns by y rows).

Sort of like a Connect-4 board.

It might need to be sloped a bit or shakeable.

In the end, although you don't know how many marbles you started with you can ultimately know what it factors into.

Another note is that the sidewall really only need be moveable in prime number increments.

A final note is that the sidewall need not move out any farther than making the whole thing a square because if this happens, it means you put some prime number of marbles in, therefore it will never factor into anything but a single column.

If the objects are not round, then I found a way to replicate this manually, with piles but it's sort of OCD at its finest...