greatest common divisor

Definitions

The largest positive integer (respectively polynomial, element of a given ring) that is a divisor of each of a given set of integers (respectively polynomials, elements of a given ring).

Equivalents

Examples

“The greatest common divisor of 66, 30 and 18 is 6.”

“1974, John M. Peterson, Basic Concepts of Elementary Mathematics, Prindle, Weber & Schmidt, page 148, Euclid's algorithm is a process⟳ for finding the greatest common divisor of any two whole numbers.”

“Suppose⟳ (a#95;0,a#95;1,#92;dots,a#95;n)#92;in#92;Z we say⟳ (a#95;0,a#95;1,#92;dots,a#95;n) is primitive if the greatest common divisor of a#95;0,a#95;1,#92;dots,a#95;n is 1.”

“This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm.[…]As one of the fundamental algebraic problems with a long history, finding the greatest common divisor (GCD) of univariate polynomials is an indispensable component of many algebraic computations besides being an important problem in its own⟳ right.”

CEFR level