These numbers aren’t arbitrary, they are from different base numbering systems.
60 can easily divide by 2, 3, 4, 5, 6, and 10.
12 can easily divide by 2, 3, 4, and 6 (notice how much overlap there is).
10 only divides easily by 2 and 5. Common fractions like 1/4 or 1/3 now require decimals.
Basically, base 12 and base 60 make it significantly easier to think and work in common fractions.
It is also historically significant, as base 12 used to be more common than modern base 10. Our timekeeping system dates back to the ancient Babylonians, who worked in base 12. This influence is still felt in other places, such as the fact that eleven and twelve have unique names in many languages rather than following the same pattern as everything that comes after them.
These numbers aren’t arbitrary, they are from different base numbering systems.
60 can easily divide by 2, 3, 4, 5, 6, and 10.
12 can easily divide by 2, 3, 4, and 6 (notice how much overlap there is).
10 only divides easily by 2 and 5. Common fractions like 1/4 or 1/3 now require decimals.
Basically, base 12 and base 60 make it significantly easier to think and work in common fractions.
It is also historically significant, as base 12 used to be more common than modern base 10. Our timekeeping system dates back to the ancient Babylonians, who worked in base 12. This influence is still felt in other places, such as the fact that eleven and twelve have unique names in many languages rather than following the same pattern as everything that comes after them.