We do not know definitely how base 60 came to be used. The suggestion may have come from the systems of weight measures. Suppose we have a system of weight measures with values in it having the ratios.
1/2, 1/3, 2/3, 1, 10
Now suppose there is another system with a different unit but the same ratios, and political or social forces compel the fusing of the two systems. (We have meters and yards, for example.) If the larger unit were 60 times the smaller, then 1/2, 1/3, and 2/3 of the larger unit would be integral multiples of the smaller one. Thus the larger unit might have been adopted because it was so convenient.
