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Mathematicians like to say that 60 is a "good" number for a base because it has so many factors. That is putting the cart before the horse.

A more likely explanation is that it was used by busy farmers, traders etc. as an easy way to count large numbers of animals or vegetables by using what was always available - the human hands.

Sixty is a number arrived at when tallying using human hands.

The four fingers are to count off twelve (the thumb is used as a pointer - each finger has three segments 3x4=12).

Once you have counted off twelve you use the fingers and thumb of the other hand to keep a record (for example curl in your thumb for the first twelve, your index finger for the second twelve, the middle finger for the third twelve, the ring finger for the fourth twelve and the small finger for the fifth twelve).

When you have counted off five dozen you have sixty- 12x5=60

It was a counting system that grew out of real people in the real world addressing everyday problems.

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