Today's Useless Fact - Why are there 60 seconds in a minute and
60 minutes in an hour?

Blame the Babylonians. The Babylonians lived about 3,000 years
ago in what is now Iraq. They thought 60 was a wonderful number.
Why, only the Babylonians know. Best guess: They figured it was
magic. (The ancients had a tendency to think everything was
magic.)
Then again, maybe the Babylonians liked 60 because it could be
evenly divided (no remainder) by so many smaller numbers: 2,3,4,
5,6,10,12,15,20, and 30.

What's the big deal with dividing evenly? Simple — you avoid
fractions, as in 10 divided by 3 equals 3 and 1/3. This may be no
big deal to you, but look at it from the point of view of Joe
Babylonian. The guy lived in a mud hut and washed his underwear
in the creek. He didn't have our modern advantages: high school,
air conditioning, color television, calculators. When he saw a
fraction, he freaked. So to him, 60 was great.

~source used: "Know It All"
by Ed Zotti