Encyclopedia > Factorization

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In mathematics, factorization or factoring is the decomposition of an object into an expression of smaller objects, or factors, which multiplied together give the original. For example, the number 15 factors into primes as 3 × 5; and the polynomial x2 - 4 factors as (x - 2)(x + 2).

The aim of factoring is usually to reduce something to "basic building blocks", such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra.

Integer factorization for large integers appears to be a difficult problem. There are no known methods for solving it quickly. It is the basis of some public key cryptography algorithms.

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