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Abstract Algebra : Prime Factors and Greatest Common Divisor

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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.

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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.

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(a) Given that b > 0 and a = b q + r.

Let (a , b) = d [ greatest common divisor (g.c.d)]

Then

Where '|' stands 'Divides' i.e. 3|6 means 3 divides 6.

...

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