What is the relationship between quality of a video and highly composite numbers?

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The most common resolutions are 240p, 360p, 480p, 720p or 1080p. 3 of these 5 resolutions are highly composite numbers, namely 240, 360 and 720. Is there a reason for that or is it just a coincidence?

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Consider that most typical videos render at 30 fps. If a monitor renders at 30 fps with 240 pixels to render, than you get nice even pretty calculations that are easy to render and track. Note that each of those numbers share specific compositions. Consider 120 which is shared between them. 30 x 40 which 3x4 is a very common screen designation as wide screen is only a recently common thing. So, common screen size and common fps means that 120 is very easy to work with.