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

Math100
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Homework Statement
If c divides ab and (c, a)=d, then c divides db.
Relevant Equations
None.
This is my work.
 

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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.
 
Math100 said:
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.
 

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