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====== Function GCD ====== ====Syntax==== * **gcd** //''&rest'' integers// → //greatest-common-denominator// ====Arguments and Values==== * //integer// - an //[[CL:Glossary:integer]]//. * //greatest-common-denominator// - a non-negative //[[CL:Glossary:integer]]//. ====Description==== Returns the greatest common divisor of //integers//. If only one //integer// is supplied, its absolute value is returned. If no //integers// are given, **[[CL:Functions:gcd]]** returns ''0'', which is an identity for this operation. ====Examples==== <blockquote> (gcd) <r>0</r> (gcd 60 42) <r>6</r> (gcd 3333 -33 101) <r>1</r> (gcd 3333 -33 1002001) <r>11</r> (gcd 91 -49) <r>7</r> (gcd 63 -42 35) <r>7</r> (gcd 5) <r>5</r> (gcd -4) <r>4</r> </blockquote> ====Side Effects==== None. ====Affected By==== None. ====Exceptional Situations==== Should signal an error of type **[[CL:Types:type-error]]** if any //integer// is not an //[[CL:Glossary:integer]]//. ====See Also==== * **[[CL:Functions:lcm|Function LCM]]** ====Notes==== For three or more arguments: <blockquote> (gcd b c ... z) ≡ (gcd (gcd a b) c ... z) </blockquote>