Prove the following problems.
1-If b>0 and a = bq + r , prove that (a , b) = (b , r).
2- Prove that (ab,c) = 1 if and only if (a,c) = 1 and (b,c)=1.
Prime factors and GCD are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.