factoring

1. 1
   noununcountable

   The process of rewriting a number or algebraic expression as the product of the factors that multiply to produce it.

   Like reverse multiplication: finding which numbers multiply together to give the one you started with.

   Factoring is one of the first techniques students learn in algebra.

   The factoring of large integers underpins much of modern cryptography.

   Similarfactorization, decomposition

   Oppositeexpansion

   Note

   Mathematics separates two jobs the verb can do. Finding all the factors of 12 means listing its divisors: 1, 2, 3, 4, 6 and 12. Factoring 12 means rewriting it as a product, 2 × 2 × 3. The noun names the second job, which is usually carried on until every piece is prime or irreducible, whether the object is an integer or a polynomial.

2. 2
   verb

   Present participle of factor.

   The students are factoring large numbers during today's lesson.

   Analysts are factoring rising fuel prices into their forecasts.

   Note

   The -ing form serves both of the verb's trades. A student factoring a polynomial and a firm factoring its debts use the same transitive verb, followed by its object. In each field the gerund hardened into a noun: the algebra process and the sale of invoices. A rarer intransitive use describes something that is itself a product, as in an expression factoring into simpler parts.

3. 3
   noununcountable

   A financial arrangement in which a business sells its unpaid invoices to a third party, called a factor, at a discount in exchange for immediate cash.

   Like selling a debt someone owes you to a third party who waits to collect the full amount later.

   Factoring allowed the manufacturer to free up cash tied in unpaid invoices.

   By using factoring, the exporter received most of its invoice value within a day.

   Note

   Finance borrowed the word from an older trade. A factor was an agent, representative or consignee who handled business on another's behalf. The factor in this arrangement still works for someone else's business, by taking over its debts to collect. The roles run one way: the business factors its receivables, and the factor buys them. This sale of debt is what separates factoring from a loan made against invoices.

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