How to divide a box into $N$ number of small boxes of equal size?

Question

How can I divide a box of size $4 \times 5 \times 6$ into $32$ small boxes of equal size? I would like to know any algorithm that can do that and provide the approximate dimensions of the small box.

Thanks!!

Answer 1

If the small box has volume $abc$, then you want $4\times 5\times 6=32abc$, or $$\frac{15}{4}=abc$$ with $a,b,c>0$. There are infinitely many solutions, so i don't know what you mean by approximate dimensions, unless you want the boxes to have some specific ratios. In case of the boxes beeing cubes, $a=b=c=\sqrt[3]{\frac{15}{4}}\approx 1.55$.