From Merzbach and Boyer's "A History of Mathematics" (good read by the way, heartily recommend) -
"The decimal system, common to most civilizations, had been submerged in Mesopotamia under a notation that made fundamental to the base 60"
Why? What would compel them to do this?
This >>7779289. Merzbach and Boyer actually discuss in the opening chapters how base systems developed. There's a small section on anthropological studies that looked into the base systems used by Native Americans - most tribes used either decimal or quinary system (after the number of fingers), and that a small percentage either used a binary or ternary system. 10% used a vigesimal system (base 20). The simple conclusion is that we developed from a basic system of two's and three's, to counting with one set of fingers, or both sets, to some systems which used both fingers and toes.
But base 60 as used in Mesopotamia has no parallel.
Base 10 is ableist and reeks of thin privilege. Not everyone can see their digits due to problems with excess adipose tissue, shitlords!
Also, it's sexist and an obvious sign that math is patriarchal. See how the big, long, powerful one - very much like a phallus - precedes the round, softer, 0 which looks of course like a vagina. The 1 is thrust before the 0, saying "The penis comes before the vagina".
It is possible for people to count on their fingers to 12 using one hand only, with the thumb pointing to each finger bone on the four fingers in turn. A traditional counting system still in use in many regions of Asia works in this way, and could help to explain the occurrence of numeral systems based on 12 and 60 besides those based on 10, 20 and 5. In this system, the one (usually right) hand counts repeatedly to 12, displaying the number of iterations on the other (usually left), until five dozens, i. e. the 60, are full.
Two reasons: 60 can be divided by 2, 3, 4, 5, and 6. This can be useful for representing fractions as decimals. And this can be represented on the hand by pointing to one of the 12 knuckles on one hand's 4 fingers with one of the 5 fingers on the other hand, giving a unique representation for all 60 digits (5x12=60)
base 12 systems are very common, even English goes 12 then thirteen, inches and feet are another example.
12 is divisible by 1,2,3,4 and 6, while 10 is only divisible by 1,2 and 5 making 12 a very easy number to work with.
60 is, as another anon said, 12x5 and is therefore divisible by 5 too.