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If one uses the Euclidean algorithm and the elementary algorithms for multiplication and division, the computation of the greatest common divisor of two integers of at most n bits is O(n 2). This means that the computation of greatest common divisor has, up to a constant factor, the same complexity as the multiplication.
The greatest common divisor g of a and b is the unique (positive) common divisor of a and b that is divisible by any other common divisor c. [6] The greatest common divisor can be visualized as follows. [7] Consider a rectangular area a by b, and any common divisor c that divides both a and b exactly.
A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor. It can be fully reduced to lowest terms if both are divided by their greatest common divisor. [5] In order to find the greatest common divisor, the Euclidean algorithm or prime factorization can be used. The Euclidean algorithm is ...
Lowest common factor may refer to the following mathematical terms: Greatest common divisor, also known as the greatest common factor; Least common multiple;
The content c(P) of a polynomial P with coefficients in R is the greatest common divisor of its coefficients, and, as such, is defined up to multiplication by a unit. The primitive part pp( P ) of P is the quotient P / c ( P ) of P by its content; it is a polynomial with coefficients in R , which is unique up to multiplication by a unit.
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[3] [4] [5] The method can be summarized in two steps. Let be the given polynomial. The first step determines the multiplicity structure by applying square-free factorization with a numerical greatest common divisor algorithm. [5] This allows writing as
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