Reducing resolution ...

A K20D has a maximum resolution of 4672x3104

If I want to reduce an image file size, I need to reduce the resolution and for most a size of around 1000 pixels wide is enough.

So, what do you do? Do you choose a "standard" setting 1280x850, 1024x680, 1000x664

Or do you quarter each of the maximum to get 1168x776 and maybe halve that to 584x388?

Has anyone tried taking an image to 1200x797 and 1168x776 and then carefully, almost pixel by pixel, examining the resulting image? If so, is there a noticeable difference and which is better?

If you were to use a free bit of software such as IrfanView (brilliant IMO), then it will handle the re-size / resample for you, as well as offering you choices for retaining the proportion of crops (or not), various resampling algorithms, dpi adjustment, 'resharpen after resize' option, etc. Pretty impressive for zero dollars.

I realise that - but the user still has to choose what size. That is the question - is it better to use a fixed divisor of the original or a "random" number?

As I understand it, that is what the resampling algorithms take care of on your behalf - so that there is no problem for you to select any smaller size at all.

Thus, the answer to your question is that, using the above method, there is no 'better or worse' in this - it's entirely your choice, and no penalty attached for using 'odd' sizes.

By way of example, if you took an image, did an 'odd-shaped' crop of it, then resized the crop, you would almost certainly end up with odd numbers on either or both axes.

That happens regularly - and I can't tell the difference solely on that account.

Happy resampling!

I've done this for years for one reason or another, and generally for anything less than 50% original size it doesn't matter if its to a fixed ratio of the original image (e.g. 4288 / 4 = 1072) or to a fixed resolution (e.g. 4288 -> 1024).

Just pick whichever suits your use at the time - I'd go for a ratio if its for emailing someone, and a fixed resolution if its for publishing on the web...

If you are going to crop the image, I'd do it first at a high resolution & zoomed out, because then the scaleing/resampling algorithms will take care of the edges slightly better. And its easier...

p.s.
Only consider the Horizontal resolution, the Vertical is whatever it comes out as...!