Search results
Results from the WOW.Com Content Network
Greatest common divisor. In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is ...
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.
Thus, the GCD is 2 2 × 3 = 12. The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, [1][2] is an algorithm that computes the greatest common divisor (GCD) of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with ...
Polynomial greatest common divisor. In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous to the greatest common divisor of two integers. In the important case of univariate ...
Extended Euclidean algorithm also refers to a very similar algorithm for computing the polynomial greatest common divisor and the coefficients of Bézout's identity of two univariate polynomials. The extended Euclidean algorithm is particularly useful when a and b are coprime. With that provision, x is the modular multiplicative inverse of a ...
Greatest common divisor = 2 × 2 × 3 = 12 Product = 2 × 2 × 2 × 2 × 3 × 2 × 2 × 3 × 3 × 5 = 8640. This also works for the greatest common divisor (gcd), except that instead of multiplying all of the numbers in the Venn diagram, one multiplies only the prime factors that are in the intersection. Thus the gcd of 48 and 180 is 2 × 2 × ...
Here the greatest common divisor of 0 and 0 is taken to be 0.The integers x and y are called Bézout coefficients for (a, b); they are not unique.A pair of Bézout coefficients can be computed by the extended Euclidean algorithm, and this pair is, in the case of integers one of the two pairs such that | x | ≤ | b/d | and | y | ≤ | a/d |; equality occurs only if one of a and b is a multiple ...
17 is divided into 3 groups of 5, with 2 as leftover. Here, the dividend is 17, the divisor is 3, the quotient is 5, and the remainder is 2 (which is strictly smaller than the divisor 3), or more symbolically, 17 = (3 × 5) + 2. In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the ...