I need to resize uploaded images to a max of 300x300.

I can do a simple resize, but image quality is lousy depending upon the resizing proportions. For example, resizing 600x600 to 300x300 is great - but resizing 602x602 to 300x300 is lousy due to pixel averaging.

So, when I do it manually in an image editor, I reduce it so that pixels are evenly divided using a calculator (and sometimes by adding whitespace around an image before reducing).

I have to work out some mathematical method of doing this - does anyone have any insights before I start wrapping my brain around this problem?

TIA