prove that if gcd(a,b)=k and gdc(b,c)=k, then gcd(a,c)>=k.

Mathematics
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 prove that if gcd(a,b)=k and gdc(b,c)=k, then gcd(a,c)>=k.

Oct 1st, 2015

Thank you for the opportunity to help you with your question!

here gcd represents greatest common divisor.
gcd(a,b)=k, means a/k=0 and b/k = 0
also ,
gcd(b,c)=k, so b/k= 0 and c/k =0
so we get that a/k=0 and c/k=0
thus k is the greatest common divisor to a and c.
thus,
gcd(a,c)>=k.
Please let me know if you need any clarification for the doubts. I'm always happy to answer your questions. Looking forward to help you again. thank you. :)
Oct 1st, 2015

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