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

\[ d|a\wedge d|b\Longrightarrow d\mid\gcd(a,b).\]

Proofs: 1

Proofs: 1

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Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"