#fotd360

[afactaday]

#aFactADay2021

#360: 360 is not only a highly composite number, but a superior highly composite number. this basically means it has a lot of factors (the exact definition is really confusing :P ). to be precise, it has 6 prime factors (2^3 * 3^2 * 5) and 24 total factors. 6 and 24 are themselves also factors, which is known as being refactorable. 360 is also a colossally abundant number, which again basically means it has lots of factors (with another confusing definition). it is 5-smooth, which means all its prime factors are 5 or smaller (the smaller the n-smooth the better lol). on the other end of the spectrum from its factors, it is the sum of two twin primes (179+181) :) just an all-round amazing number :D

the mesopotamians and babylonians both recognised these magic features of 360, so used base-60 radix-10 numbers, which is also why we have 360 degrees in a circle, 3600 seconds in an hour and nothing to do with 360 days in a year.

have some OEIS references:

highly composite numbers: A002182

the number of divisors of a number: A000005

superior highly composite numbers: A002201

refactorable numbers: A033950

colossally abundant numbers: A004490

5-smooth numbers: A051037

360 is also the amount of feet that a baseballist must run to score a run.