Algorithm to get the maximum size of n squares that fit into a rectangle with a given width and height

Algorithm to get the maximum size of n squares that fit into a rectangle
with a given width and height

I am looking for an algorithm that can return the number of size of n
squares that fit into a a rectangle of a given width and height,
maximizing the use of space (thus, leaving the least amount of leftover
space for squares that do not fit). Neither the rectangle nor the squares
can be rotated.
For example, let's say I have a rectangle that is 5 inches by 7 inches,
and I need it to fit 35 squares. The algorithm needs to tell me that the
35 squares fit if they are 1 inch wide/tall (as they could be laid out
inside the rectangle in a 5 x 7 grid). Another example is if I need to
divide a rectangle 35 inches by 1 inch into 35 squares. It should still
tell me that the squares will fit if they are 1-inch wide/tall (as they
could be laid out in the rectangle in a 35 x 1 grid).
The tricky part is that sometimes there may be leftover space, as the
squares cannot be divided into partial squares. Let's say for either of
the two examples above I need to lay out 34 squares and not 35 (in which
case the answers would still be 1 inch), or maybe 33, or 7 squares. Or,
perhaps the rectangle width and height aren't whole numbers. With the
number of squares being a variable I need an algorithm that can tell me
the size of the squares for a given rectangle width and height.
Thanks for your help!