DIVISION. In mathematics. one of the four fundamental piocesses of arithmetic, the one by which we find one of tv‘o factors when the prod uct and the other factor are given. The given factor is called the dirisor, the given product is called the diridend, and the result (i.e. the required factor) is called the quotient. The definition of division leads to the following identity: dividend = divisor X quotient re mainder. If the remainder is zero, the division is said to he exact. The common symbols for division are: a 4- le: a : b, a/b. in which a is the dividend and b the divisor. Two forms of division are recognized in elementary arith meth. the one based on the idea of measurement and the other on the idea of partition. The former is the case of dividing, one number by another of the same kind. and the latter that of dividing a concrete by an abstract number.
The usual tests of the correctness of division are: (a I multiply the quotient by the divisor and add the remainder. the result equaling the dividend; (b1 compare the of nine; in the identity of division. See CliErICIN(:.
Simple of the divisibility of numbers by 2, d. 5. G. S. 9. 10, 11 are: (a) a number is divisible by 2, 4, or S if the number represented by the last digit, the last two digits, or the last three digits is din isible by 2, 4, respectively; Ih a number is divisible by .1 if it ends in 0 or he 10 if it ends in 0: le) a number is divisible by !I, or by 3, if the -um of its digits 1-- 41i%•trs, or by :3. resp(.ctively, and by t; if it is even, and the sum of its digits is divis ible by 3; Id) a number is divisible by II if the ditreren•e between the sum of the digits in the dd and in the even places is divisible by II. The simplest test of the divisibility by algebraic binomials is that of the remainder theorem (q.v.). The division of large numbers is gener ally facilitated by the use of logarithms (q.v.). For the origin of the present method of division and for improved forms, see Anent NIETIC.