24-360

"If you ever wondered why '24' hours in a day, and not some other, arbitrarily chosen number, or why there are '360' degrees in a circle instead of some other number or some other unit, the reason stems from how handily 24 and 360 break down into many useful fractional parts using integers. For example, 1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 90, 120, 180, and 360 are ALL factors of 360, while 1, 2, 3, 4, 6, 8, 12, and 24 are ALL factors of 24. Few numbers break down into as many handy factors, and these numbers have a lot of factors in common. So while one might use another arbitrary number, chances are such a number would be less useful when considering fractions of the whole. 1/2, 1/3, 1/4, 1/6, 1/8, 1/9, 1/10, 1/12, 1/15, 1/18, 1/20, 1/24, 1/30, 1/36, 1/40, 1/45, 1/60, 1/90, 1/120, and 1/180 are all handy, though the ones under 1/12 are even more so. For similar reasons, one 'dozen' is a handy unit in which to sell items. So regardless of how long a planet's day is in actual time, breaking it up into 24 units is a handy thing to do. Further divisions in 60 minutes and 60 seconds uses these same numbers and handy factors." (quotation © January of 2000 by James L. R. Beach)