so you're given appet width, height and total number of grid cells?  can't be solved analytically yet.

you need to specify at least one other value, call it 'aspect', then you can solve it.  (of either the # of cols/rows in the grid, or of the resulting width/height of the cells themselves)

for example, say you need 100 cells in a 2000x500 image.  if you specify "square aspect rows/cols", then the number of rows/cols is sqrt(100)=10, and their width/height is 2000w/10c=200px x 500h/10r=50px height.

if you instead specify "square aspect width/height", then the area of each cell must be (2000x500)/100=10000, so their w/h must be sqrt(10000)=100, so # of cols/rows is 2000/100=20cols and 500/100=5rows.

(of course i picked "pretty" values that work out nicely, you'll have to deal with rounding issues, and you need not use 'square' asepct)

but you can see that 10x10@200x50 and 20x5@100x100 could BOTH be valid answers, so you need to provide more info to resolve which is the "right" solution.