Can anyone please check my work of this proof? (Number Theory)

[Math100]

Homework Statement

If c divides ab and (c, a)=d, then c divides db.

Relevant Equations

None.

This is my work.

 

[jambaugh]

I'm not clear on your "it follows that..." in the 2nd sentence. Better to say "then c = ud, a = vd and (u,v)=1." and work from there.

 

[Mark44]

Homework Statement:: If c divides ab and (c, a)=d, then c divides db.
Relevant Equations:: None.

This is my work.

@Math100, in future threads, please post your work as text, rather than as a photo in a pdf file.