Publication Date



Technical Report: UTEP-CS-19-106


At present, we mostly use decimal (base-10) number system, but in the past, many other systems were used: base-20, base-60 -- which is still reflected in how we divide an hour into minutes and a minute into seconds -- and many others. There is a known explanation for the base-60 system: 60 is the smallest number that can be divided by 2, by 3, by 4, by 5, and by 6. Because of this, e.g., half an hour, one-third of an hour, all the way to one-sixth of an hour all correspond to a whole number of minutes. In this paper, we show that a similar idea can explain all historical number systems, if, instead of requiring that the base divides {\it all} numbers from 2 to some value, we require that the base divides all but one (or all but two) of such numbers.