Multiplication

Article By:

Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.

Last reviewed:June 2020

DOI:https://doi.org/10.1036/1097-8542.438700

One of the fundamental operations of arithmetic and algebra. The use of the symbol ×, commonly employed in arithmetic to denote multiplication, is attributed to the English mathematician William Oughtred (1574–1660). Because of its resemblance to the letter x, it is rarely used in algebra, where multiplication is frequently denoted by a dot (as in a · b) or, most often, merely by juxtaposition of letters (for example, ab). Multiplication of numbers (real or complex) is associative, a(bc) = (ab)c; commutative, ab = ba; and distributive with respect to addition, a(b + c) = ab + ac; but the term has been extended to denote binary operations on many other kinds of objects, and these operations need not possess all the properties of ordinary multiplication listed above (for example, multiplication of matrices is not commutative). Much effort was formerly expended in the computation and design of multiplication tables, and the related endeavor of tables of prime numbers. (A whole number is a prime if it is not exactly divisible by any whole number other than itself and 1.) The largest known prime (as of July 2011) is the number 2^43,112,609–1, which has 12,978,179 digits. This prime was discovered in 2008 by implementing a sophisticated prime discovery algorithm on a computer. All of the largest known primes are numbers of the form 2^p − 1, where p itself is a prime number. Prime numbers of this form are called Mersenne numbers. See also: Addition; Algebra; Division; Numbering systems; Number theory; Subtraction

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