365 days is the (approximate) number of times the Earth rotates about its axis during the time take for it to go around the Sun. Because that is rounded to the nearest full rotation (the real number is about 365.25, we sometimes need an extra day to makes it up, which is where leap years come from.
For 24 hours in a day, I’m not entirely sure, but it has the benefit of being divisible into a large number of sub-sections of the day, 1,2,3,4,6,8,12 all do into 24 hours, which makes splitting the day up nice and easy.
The 24 hour day was devised by the ancient Egyptians – the daytime was divided into 10 hours, with additional twilight hour at the beginning and another at the end, making 12 hours total. Night-time was divided into 12 hours, based on the observations of the stars.
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