Proposition: 7.23: Divisor of One of Coprime Numbers is Coprime to Other
(Proposition 23 from Book 7 of Euclid's “Elements”)
If two numbers are prime to one another then a number measuring one of them will be prime to the remaining (one).
* Let $A$ and $B$ be two numbers (which are) prime to one another, and let some number $C$ measure $A$.
* I say that $C$ and $B$ are also prime to one another.
Modern Formulation
If $A$ and $B$ are coprime and $C$ is a divisor of $A$, then $C$ and $B$ are also coprime.
Table of Contents
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016