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Because we based our time system on numbers that were convenient.

Not only is 60 a multiple of 10, but you can also divide it into thirds and quarters.

60 is the smallest number with all of those properties.
For historical reasons. In the remote past, somebody used 60 subdivisions, probably because of the large number of factors this number has, and it is now difficult to change this, since everybody is accustomed to the current system. Decimal subdivisions of a day have been proposed, but never gained much popularity.

In fact counting in 60s is ancient and spread across a number of cultures - see link.

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Q: Why are there 60 seconds to a minute?
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