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Wikipedia's list of numeral systems lists only $10,20,60$ as having been used in history. There are about twenty-five sets of symbols there used by different groups of people, but only three different bases. I'm a little surprised that, even if some of these civilizations learned about positional notation from others and did not independently discover it, they changed up the symbols without exploring whether a different base could be used. I would have thought that base $30$ would be a decent candidate since it multiplies the first three primes (there are advantages with respect to the quantity of terminating rational numbers and convenient divisibility rules) while having only half the number of distinct symbols as $60,$ which has been used by Babylonians, and the number of days in a lunar month is 29-30 days (see Arabic calendar)

Question: Has there been a large group of people that worked with a base other than $10,20,60$ for day-to-day activities?

I have read this thread and it also mentions bases $10,20,60,$ but no other significant ones. There is a TED-Ed talk about on this subject as well, but it doesn't mention any others. excluding the usage of bases that are powers of $2$ for purposes related to computers.

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  • $\begingroup$ One large group is computer programmers who use base 2, another large group, to which you probably belong uses base 24 (1 day=24 hours). Americans also use bases 12 and 16 in their length and force measures. $\endgroup$ – Alexandre Eremenko Jul 10 at 19:49
  • $\begingroup$ @AlexandreEremenko Do the 24 and 12 or 16 really count as bases? We don't have additional symbols in use past 9. The 24 hour system is more like modular arithmetic than a base system. $\endgroup$ – Favst Jul 10 at 19:53
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    $\begingroup$ Wikipedia: "Languages using duodecimal number systems are uncommon. Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Gure-Kahugu), Piti, and the Nimbia dialect of Gwandara and the Chepang language of Nepal are known to use duodecimal numerals." One could also argue that the roman system was "quinquenal" (X is actually v and ^; the next symbol is L for 50). A circle is divided by his radius in 6 parts which suggests an explanation for 60 but also for 12 or 24. $\endgroup$ – sand1 Jul 10 at 19:57
  • $\begingroup$ @Facst: when you count what time and date will be in 100 hours from now, you use 24 as a base. When one buys 1 1/2 pounds of cheese at $28.99 per ounce, she uses 16 as a base. $\endgroup$ – Alexandre Eremenko Jul 10 at 20:10
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    $\begingroup$ People who are doing computations are not "thinking" in terms of any positional system, it is a technical contrivance. They just follow prescribed algorithms, decimal or otherwise, sometimes on paper, sometimes on abacus, sometimes in their head. Ancient Chinese and modern programmers did it with hexadecimals, Yuki used octals, and the Telefol used heptavigesimals. But bases 10, 20 and 60 are the most common. $\endgroup$ – Conifold Jul 10 at 22:41
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Wikipedia:

Languages using duodecimal number systems are uncommon. Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Gure-Kahugu), Piti, and the Nimbia dialect of Gwandara and the Chepang language of Nepal are known to use duodecimal numerals.

Also:

It is thought that Nimbia, which is isolated from the rest of Gwandara, acquired its duodecimal system from neighboring East Kainji languages. It is duodecimal even to powers of base twelve.

It also appears that many ancient progenitors of Indo-European languages were based on 4 or 12, due to rembant number words that don't line up with a purely decimal system:

Germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they come from Proto-Germanic *ainlif and *twalif (meaning, respectively one left and two left), suggesting a decimal rather than duodecimal origin.

Wikipedia's primary source appears to be this article by Shuji Matsushita.

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