factor

—factorable, adj. —factorability, n. —factorship, n.

/fak"teuhr/, n.

1. one of the elements contributing to a particular result or situation: Poverty is only one of the factors in crime.

2. Math. one of two or more numbers, algebraic expressions, or the like, that when multiplied together produce a given product; a divisor: 6 and 3 are factors of 18.

3. Biochem. any of certain substances necessary to a biochemical or physiological process, esp. those whose exact nature and function are unknown.

4. a business organization that lends money on accounts receivable or buys and collects accounts receivable.

5. a person who acts or transacts business for another; an agent.

6. an agent entrusted with the possession of goods to be sold in the agent's name; a merchant earning a commission by selling goods belonging to others.

7. a person or business organization that provides money for another's new business venture; one who finances another's business.

8. See factor of production.

9. Scot. the steward or bailiff of an estate.

v.t.

10. Math. to express (a mathematical quantity) as a product of two or more quantities of like kind, as 30 = 235, or x² - y² = (x + y) (x - y). Cf. expand (def. 4a).

11. to act as a factor for.

v.i.

12. to act as a factor.

13. factor in or into, to include as an essential element, esp. in forecasting or planning: You must factor insurance payments into the cost of maintaining a car.

[1400-50; late ME facto(u)r < L factor maker, perpetrator, equiv. to fac(ere) to make, do + -tor -TOR]

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In multiplication, one of two or more numerical or algebraic components of a product.

A whole number's factors are the whole numbers that divide evenly into it (e.g., 1, 2, 3, 4, 6, and 12 are factors of 12). To factor a counting number means to break it down into its prime number factors. To factor a polynomial is to find its prime polynomial factors, a basic procedure for solving algebraic equations. According to the fundamental theorem of arithmetic, the prime factorization of any number or polynomial is unique.

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▪ mathematics

      in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12. A positive integer greater than 1, or an algebraic expression, that has only two factors (i.e., itself and 1) is termed prime; a positive integer or an algebraic expression that has more than two factors is termed composite. The prime factors of a number or an algebraic expression are those factors which are prime. By the fundamental theorem of arithmetic, except for the order in which the prime factors are written, every whole number larger than 1 can be uniquely expressed as the product of its prime factors; for example, 60 can be written as the product 2·2·3·5.

      Methods for factoring large whole numbers are of great importance in public-key cryptography, and on such methods rests the security (or lack thereof) of data transmitted over the Internet. Factoring is also a particularly important step in the solution of many algebraic problems. For example, the polynomial equation x² − x − 2 = 0 can be factored as (x − 2)(x + 1) = 0. Since in an integral domain a·b = 0 implies that either a = 0 or b = 0, the simpler equations x − 2 = 0 and x + 1 = 0 can be solved to yield the two solutions x = 2 and x = −1 of the original equation.

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