Meaning of FACTOR in English

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. With the exception of 1, a positive integer 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 integer can be uniquely expressed as the product of its prime factors; for example, 60 can be written as the product 2235. Factoring is 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 ab = 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 equation.

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