How to calculate the proportions of N images so that they occupy the entire area of ​​a certain size?

Question

Images

I want to get the Nth number of server images with a curl, and then "glue" them into 1, while changing their sizes, so that I get a table with several columns and rows.
An example of how to do it manually: in Photoshop, we can create an image, throw other images there as new layers, and then reduce their size and position them.
Task: We have an image of 600x400 pixels, on which 6 images should be located. (From now on, I don’t know how to calculate). You can place 3 images in each line, then 600/3 is the maximum image width and 400/2 is the maximum height.
How to calculate the optimal number of rows and columns of images?

Answer 1

How to calculate the optimal number of rows and columns of images

What is the optimization criterion?

Answer 2

Is 100% coverage important?