How time works
Why are there 60 minutes in an hour?
The answer runs through Babylonian base-60 mathematics, Greek astronomy and medieval clockmaking.
Sixty divides cleanly
Sixty has many divisors: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. That makes it unusually convenient for splitting a circle, an hour or an angle into common fractions without decimals.
Astronomy carried base 60 forward
Babylonian mathematics used a sexagesimal, or base-60, system. Greek and later Islamic astronomers inherited sexagesimal subdivisions for angles, and the same language of first and second small parts became minutes and seconds.
Clocks made the convention everyday
Early public clocks chiefly marked hours. As mechanisms improved, minute and then second hands made astronomical subdivisions visible in daily life, fixing 60 minutes per hour and 60 seconds per minute as the civil convention.