greatest common divisor

Definitions

1. 1

   The largest positive integer (respectively polynomial, element of a given ring) that is a…

   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).

   • 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.

The neighborhood

• antonymleast common multipleantonym(s) of “largest number that divides each of a set of positive integers”