Corollary: 7.02: Any Divisor Dividing Two Numbers Divides Their Greatest Common Divisor
(related to Proposition: 7.02: Greatest Common Divisor of Two Numbers  Euclidean Algorithm)
(Corollary to Proposition 2 from Book 7 of Euclid's “Elements”)
So it is manifest, from this, that if a number measures two numbers then it will also measure their greatest common measure. (Which is) the very thing it was required to show.
Modern Formulation
See greatest common divisor, formally
\[ da\wedge db\Longrightarrow d\mid\gcd(a,b).\]
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"