Divisor

(redirected from Proper divisor)
Also found in: Dictionary, Thesaurus, Encyclopedia.

Divisor

Used in construction of stock indices. Suppose there 10 stocks in an index, each worth \$10 and the index is at 100. Now suppose that one of the stocks must be replaced with another stock that is worth \$20. If no adjustment is made to the divisor, the total value of the index would be110 after the swapping. yet there should be no increase in value because nothing has happened other than switching the two constituents. The solution is to change the divisor; in this case from 1.00 to 1.10. Note that the value of the index, 110/1.1, is now exactly 100 - which is where it was prior to the swap.

Divisor

In division, the number by which another number if divided. For example, in the equation 8 / 4 = 2, the divisor is 4. This is used in indexes to account for stock splits and dividends. See also: Dow divisor.
References in periodicals archive ?
Figure 4: The first seven members of the aliquot sequence of 30: sum of proper integer proper divisors divisors 30 1, 2, 3, 5, 6, 10, 15 42 42 1, 2, 3, 6, 7, 14, 21 54 54 1, 2, 3, 6, 9, 18, 27 66 66 1, 2, 3, 6, 11, 22, 33 78 78 1, 2, 3, 6, 13, 26, 39 90 90 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 144 45 144 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 259 24, 36, 48, 72 What is striking about the sequence {30, 42, 54, 66, 78, 90, 144} is that the Greatest Common Divisor (CGD) for its 7 members is 6, which is a 'perfect number' because it equals the sum of its proper divisors (1+2+3=6).
Consider first 12: The sum of the proper divisors is 16, which does not have 6 as a divisor.
The proper divisors are p, q, [p.sup.2], pq, and since S([p.sup.2]) = 2p, S(pq) = q, (4) implies the equation
Since the proper divisors of n = [2.sup.k]p are 2, [2.sup.2],..., [2.sup.k], p, 2p, [2.sup.2]p,..., [2.sup.k-1]p, one has

Site: Follow: Share:
Open / Close