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.
See greatest common divisor, formally
\[ d|a\wedge d|b\Longrightarrow d\mid\gcd(a,b).\]
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Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"