Editing Binary GCD algorithm (section)

==Historical description==
An algorithm for computing the GCD of two numbers was known in ancient China, under the [[Han dynasty]], as a method to reduce fractions:

{{quote| title= Fangtian – Land surveying| source=''[[The Nine Chapters on the Mathematical Art]]'' |text=If possible halve it; otherwise, take the denominator and the numerator, subtract the lesser from the greater, and do that alternately to make them the same. Reduce by the same number.}}

The phrase "if possible halve it" is ambiguous,<ref name="Knuth98"/>
* if this applies when ''either'' of the numbers become even, the algorithm is the binary GCD algorithm;
* if this only applies when ''both'' numbers are even, the algorithm is similar to the [[Euclidean algorithm]].