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  2. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    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.

  3. Greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Greatest_common_divisor

    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.

  4. Polynomial greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Polynomial_greatest_common...

    There are several ways to find the greatest common divisor of two polynomials. Two of them are: Factorization of polynomials, in which one finds the factors of each expression, then selects the set of common factors held by all from within each set of factors. This method may be useful only in simple cases, as factoring is usually more ...

  5. Extended Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Extended_Euclidean_algorithm

    In computer algebra, the polynomials commonly have integer coefficients, and this way of normalizing the greatest common divisor introduces too many fractions to be convenient. The second way to normalize the greatest common divisor in the case of polynomials with integer coefficients is to divide every output by the content of r k ...

  6. Polynomial long division - Wikipedia

    en.wikipedia.org/wiki/Polynomial_long_division

    The result R = 0 occurs if and only if the polynomial A has B as a factor. Thus long division is a means for testing whether one polynomial has another as a factor, and, if it does, for factoring it out. For example, if a root r of A is known, it can be factored out by dividing A by (x – r).

  7. General number field sieve - Wikipedia

    en.wikipedia.org/wiki/General_number_field_sieve

    Now the product of the factors a − mb mod n can be obtained as a square in two ways—one for each homomorphism. Thus, one can find two numbers x and y, with x 2 − y 2 divisible by n and again with probability at least one half we get a factor of n by finding the greatest common divisor of n and x − y.

  8. What is a factor rate and how to calculate it - AOL

    www.aol.com/finance/factor-rate-calculate...

    Step 3: Divide the result by your repayment period Step 4: Multiply the result by 100 Here’s an example using the $100,000 loan with a factor rate of 1.5 and a two-year (730 days) repayment period:

  9. Gauss's lemma (polynomials) - Wikipedia

    en.wikipedia.org/wiki/Gauss's_lemma_(polynomials)

    If () is a monic polynomial in one variable with coefficients in a unique factorization domain (or more generally a GCD domain), then a root of that is in the field of fractions of is in . [ note 5 ] If R = Z {\displaystyle R=\mathbb {Z} } , then it says a rational root of a monic polynomial over integers is an integer (cf. the rational root ...