Let a soft keyboard provide 24 buttons. 24 is a nice number because it can be laid out in many rectangular areas, depending on (say) orientation: 1x24, 2x12, 3x8, 4x6.
We need to vote some letters off the island, relegating them to a second screen. More than just two, if we want spacebar and maybe some common punctuation on the main keyboard. Maybe spacebar is double sized or more, because it is important, triggering autocorrect.
30 is the next number with lots of factors. We gain divisibility by 5 but lose divisibility by 4, so probably not worth it.
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