Note that both 12 and 60 are such numbers.
[1] https://en.wikipedia.org/wiki/Highly_composite_number
Also it looks like the Babylonian is a composite system, where the 'digits' are represented in base 10 (the 10s use a different digit, but it doesn't matter). They could alternatively use base 12 for this digit.
http://searchfox.org/mozilla-central/source/gfx/src/AppUnits...
Better to use duodecimal.
> Better to use duodecimal.
Assuming you mean the decimals 0.1 and 0.2, they can't be represented as terminating duodecimals (which is different from not being represented accurately!), either. Whatever base you choose, someone's favourite fraction won't have a terminating expansion.
Of course in any base there will be some non-terminating representations of rational numbers, so changing the base of the floating point system changes which numbers these are but does not eliminate them.
In base 10, you can quickly spot multiples of 2, 5, and ten (or alternatively, reduce any number module 2, 5, or 10).
... and 4 and 6 and 10. (and 12, 15, 30, 60)