Corollary 3

Tag 06AC, permanent. Cite it as [Bourbaki, Tag 06AC].

— Let w be a common factor of f and g. For w to be a gcd off and g it is necessary and sufficient that $f/w$ and $g/w$ are relatively prime. This follows from Cor. 2.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.