Proposition: 7.24: Integer Coprime to all Factors is Coprime to Whole
(Proposition 24 from Book 7 of Euclid's “Elements”)
If two numbers are prime to some number then the number created from (multiplying) the former (two numbers) will also be prime to the latter (number).
Modern Formulation
If $A$ and $B$ are both coprime to $C,$ then also the product $AB$ is coprime to $C.$
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3
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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