 InvestHub.com's Finance Dictionary and Glossary of Investment Terms divisor Definition 1.
A value used to ensure that the numerical value of an index does not change despite developments that alter its composition. The raw value of the index is divided by the divisor in order to calculate the normalized value. The divisor changes when the makeup of the index changes and neutralizes the change.  Definition 2.
Used in construction of stock indices. Suppose you have 10 stocks in an index, each worth $10 and the index is at 100. Now suppose you want to replace one of the stocks with another stock (reshuffling happens). Suppose that the new stock to be included is worth $20. So the total value of the index is 110 after the swapping. But we really shouldn't have an increase in value because nothing has happened  other than switching two constituents. So, what people do is to change the divisor. In this case, the divisor goes from 1 to 1.10. Notice that the value of the index, 110/1.1 is now exactly 100  which is where we began from. 

