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It is believed that the ancient Babylonians divided the circle into 360 degrees. 360 has the advantage that it is divisible by many of the numbers used for fractions used in everyday life such as 2, 3, 4, 5, 6, 8, 9, 10, 12 and 60. The fact the earth did a complete circle around the sun in nearly 360 days might have helped.

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