Proposition: 7.03: Greatest Common Divisor of Three Numbers
(Proposition 3 from Book 7 of Euclid's “Elements”)
To find the greatest common measure of three given numbers (which are) not prime to one another.
* Let $A$, $B$, and $C$ be the three given numbers (which are) not prime to one another.
* So it is required to find the greatest common measure of $A$, $B$, and $C$.
See the greatest common divisor of more than two numbers.
- 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.
- Euclid does not provide a definition of the greatest common divisor, he only provides a method to calculate it.
- The modern definition is a generalization of the greatest common divisor of two numbers for any finite number of integers, not only of three integers.
Table of Contents
Thank you to the contributors under CC BY-SA 4.0!
Adapted from CC BY-SA 3.0 Sources:
- Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016
- Health L. Thomas (Transl.): "Euclid's Elements - all thirteen books", Green Lion Press, 2013,