conclusion of factorisation
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In mathematics, factorization (also factorisation in some forms of British English) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5is a factorization of the integer 15, and (x – 2)(x + 2) is a factorization of the polynomial x2 – 4.
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In mathematics, factorization (also
factorisation in some forms of British English) or factoring consists of writing a number or another
mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and (x – 2)( x + 2) is a factorization of the polynomial x 2 – 4.
Factorization is not usually considered meaningful within number systems possessing division , such as the real or complex numbers , since any can be trivially written as
whenever is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator.
Factorization was first considered by
ancient Greek mathematicians in the case of integers. They proved the
fundamental theorem of arithmetic , which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1. Moreover, this factorization is unique up to the order of the factors. Although integer factorization is a sort of inverse to multiplication, it is much more difficult algorithmically, a fact which is exploited in the RSA cryptosystem to implement public-key cryptography
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factorisation in some forms of British English) or factoring consists of writing a number or another
mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and (x – 2)( x + 2) is a factorization of the polynomial x 2 – 4.
Factorization is not usually considered meaningful within number systems possessing division , such as the real or complex numbers , since any can be trivially written as
whenever is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator.
Factorization was first considered by
ancient Greek mathematicians in the case of integers. They proved the
fundamental theorem of arithmetic , which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1. Moreover, this factorization is unique up to the order of the factors. Although integer factorization is a sort of inverse to multiplication, it is much more difficult algorithmically, a fact which is exploited in the RSA cryptosystem to implement public-key cryptography
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