Resolutions tend to be a power of 2 (or a multiple of a power of 2 that is as large as possible), possibly because 3D graphics renderers often use a technique called mipmapping, and many image formats as well as video codecs also process the image in block sizes that are powers of 2 like 8x8, 16x16...

Obviously 1360:765 is precisely 16:9, but 765 isn't divisible by any power of 2, while 768 can be divisible by 256 (2^{8}), so 768 for the height is a better choice.

`768/(16/9) = 1365.333...`

, so if you round it up, you'll get a common resolution that is 1366x768, which is very close to 16:9. But again, 1366 is only divisible by 2 so some screen manufacturers use 1360x768 instead since 1360 is divisible by 16 which is much better. 1360/768 = 1.7708333... which approximates 16/9 to about 2 decimal places, and that's enough.

Many 12MP cameras have effective resolution of 4000x3000, and when shooting in 16:9, instead of using the resolution 4000x2250 which is exactly 16:9, they use 4000x2248 because 2248 is divisible by 8 (which is the common block size in many video codecs), and 2500 is divisible by 4.

Some Kodak cameras use 4000x2256 too, since 2256 is divisible by 16, and 4000/2256 still approximates 16/9 to about 2 decimal places. If shooting in 3:2 they'll use 4000x2664, not 4000x2667 which is closer to 3:2, for the same reason.

And this is true for other resolutions too. You won't find any image resolutions that are odd. Most will be at least divisible by 4 - or better, 8. The full HD resolution, 1920x1080, has a height not divisible by 16, so many codecs will use 1920x1088 instead, then crop it down when displaying or after processing. But sometimes it's not cropped so you can see there are many 1920x1088 videos on the net. Some files are reported as 1080 but actually 1088 inside.

You may also find the option to crop 1088 to 1080 in various video decoder's settings.