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For all $k > 0,\ k\in \Bbb Z$ . Prove $$\gcd(k*a,\ k*b) = k *\gcd(a,\ b)$$

I think I understand what this wants but I can't figure out how to set up a formal proof. These are the guidelines we have to follow

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Martin Sleziak
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Mikky Davey
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    I've noticed that you have asked quite a few questions recently. I wanted to make sure that you are aware of the quotas 50 questions/30 days and 6 questions/24 hours, so that you can plan posting your questions accordingly. (If you try to post more questions, StackExchange software will not allow you to do so.) For more details see meta. –  Apr 22 '14 at 03:35
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    ok thank you for warning me :) I wasn't aware of the limit – Mikky Davey Apr 22 '14 at 03:52
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    This questions was shown (as the top one) among related questions on the right: http://math.stackexchange.com/questions/202397/how-to-prove-that-z-cdot-textgcda-b-textgcdza-zb – Martin Sleziak Apr 22 '14 at 05:21

1 Answers1

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Hint: Start with the fact that $\gcd(k a, k b)$ is the minimal positive value of $s k a + t k b$, and factor out $k$.

vonbrand
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