Proposition: 7.02: Greatest Common Divisor of Two Numbers  Euclidean Algorithm
(Proposition 2 from Book 7 of Euclid's “Elements”)
To find the greatest common measure of two given numbers (which are) not prime to one another.
* Let $AB$ and $CD$ be the two given numbers (which are) not prime to one another.
* So it is required to find the greatest common measure of $AB$ and $CD$.
Modern Formulation
See greatest common divisor.
Notes
 Euclid does not provide a definition of the greatest common divisor, he only provides a method to calculate it.
 Nowadays, it is not necessary to require that the numbers are not prime to one another to be able to find their greatest common divisor. There exists also a correct and efficient algorithm for finding the \(\gcd\) of any two integers, at least one of which does not equal \(0\).
 The contemporary definition of the greatest common divisor not given in Euclid's Elements has the advantage that \(gcd(0,0)\) is welldefined: \(0\) is the only integer, which is divisible by all other integers. Therefore, \(\gcd(0,0)=0\).
Table of Contents
Proofs: 1 Corollaries: 1
Mentioned in:
Proofs: 1 2
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"