Our measures for angles and for time descend from the base 60 Babylonian system, whereas base 10 descends from the ancient Egyptian system.
For dealing with heterogeneous bases, as with measuring in imperial units, take a look at the fraction notation in Fibonacci’s book. https://en.wikipedia.org/wiki/Liber_Abaci#Fibonacci.27s_nota...
24 is similarly divisible by 2,3,4,6,8,12, whereas 25 is only evenly divisible by 5. So those odd-looking "constants" are good for something after all.