What about octal? It's more that much more divisible than base 10 (10 divides 1,2,5,10 ... 8 divides 1,2,4,8) but as a power of 2 it has certain advantages to use as a base system.
The reason I say that instead of a more factorable system like duodecimal (12 divides 1,2,3,4,6,12) or sexagesimal like the Babylonians used (60 divides 1,2,3,4,5,6,10,12,15,20,30,60) is because the octal system would be easy to learn for kids. If you just stick your hands out in front of you and tuck your thumbs under your palms, there ya go, you have digits 0-7.
But it's not that worth it since octal doesn't really provide that many more advantages over decimal (it's actually less efficient in terms of how many digits, requiring something like log(10)/log(8) times as many digits), other than breeding a future generation of good programmers because of how easy it'd be to convert to binary or hexadecimal
I'm a fan of going back to sexagesimal if everyone can remember a bunch of symbols. I think binary is the most 'pure' but sexagesimal is on the opposite end of the spectrum. Think about doing fractions in sexagesimal, it'd be very easy, much easier than base 10.
"one third" in decimal = 0.3333333333333333333333333333333...etc
"one third" in sexagesimal = 0.[20] where [20] is a single digit representing our decimal "20"
lots of other fractions could be expressed conveniently without so many repeating digits:
fraction :: sexagesimal version
1/2 :: 0.[30]
1/3 :: 0.[20]
1/4 :: 0.[15]
1/5 :: 0.[12]
1/6 :: 0.[10]
1/7 :: 0.[8][34][17]...(repeats those 3 digits forever) ... this one is gonna be messy no matter what base system is used pretty much
1/8 :: 0.[7][30] (think [7.5] being half of [15] which is 1/4)
1/9 :: 0.[6][40] (think [6 + 2/3] being a third of [20] which is 1/3)
1/10 :: 0.[6]
etc. I'd rather teach a kid sexagesimal fractions than decimal versions. Then again the major drawback is having so many symbols. So I'm gonna have to go with binary... its purity is appealing, despite being the most inefficient (digits per number) of the systems