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# zui4 da4 gong1 yue1 shu4 han2 shu4 (GreatestCommonDivisorFn)

(GreatestCommonDivisorFn number1 number2 ... number) returns the greatest common divisor of number1 through number.

## Ontology

SUMO / NUMERIC-FUNCTIONS

## Class(es)

 zhong3 lei4

ke3 ji4 cheng2 guan1 xi4

han2 shu4
 bian4 yi4 yuan2 shu4 guan1 xi4

zui4 da4 gong1 yue1 shu4 han2 shu4

## Coordinate term(s)

zhi3 ding4 han2 shu4  zui4 xiao3 gong1 bei4 shu4 han2 shu4  xu4 lie4 han2 shu4  mao2 dun4 shu3 xing4  wu2 jiao1 ji2 fen1 jie3  wu2 jiao1 ji2 guan1 xi4  qiong2 jin4 de5 shu3 xing4  qiong2 jin4 de5 fen1 jie3  cheng2 li4  fen1 ge1

## Axioms (2)

• if " de5 zui4 da4 gong1 yue1 shu4" deng3 yu1 number,
• then for all element holds: if element shi4 "()" de5 yi1 cheng2 yuan2, then "element qu3 yu2 shu4 number" deng3 yu1
• .
(=>
(equal
(GreatestCommonDivisorFn @ROW)
?NUMBER)
(forall
(?ELEMENT)
(=>
(inList
?ELEMENT
(ListFn @ROW))
(equal
(RemainderFn ?ELEMENT ?NUMBER)
0))))

• if " de5 zui4 da4 gong1 yue1 shu4" deng3 yu1 number,
• then there doesn't exist greater so_that_not greater (bu2) da4 yu1 number and for all element holds: if element shi4 "()" de5 yi1 cheng2 yuan2, then "element qu3 yu2 shu4 greater" deng3 yu1
• .
(=>
(equal
(GreatestCommonDivisorFn @ROW)
?NUMBER)
(not
(exists
(?GREATER)
(and
(greaterThan ?GREATER ?NUMBER)
(forall
(?ELEMENT)
(=>
(inList
?ELEMENT
(ListFn @ROW))
(equal
(RemainderFn ?ELEMENT ?GREATER)
0)))))))