Where do I start?
I don't really understand what the difference is between the two. It seems so logic to me that I don't know how wich parts I should explain.
How to start, What is there to be shown?
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1What is your definition of $\gcd(a,b)$? – Jason DeVito - on hiatus Nov 18 '13 at 21:50
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Can you give us a precise definition from your textbook of GCD(a,b)? – BaronVT Nov 18 '13 at 21:50
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You are right it is obvious. I guess you can write $gcd(a,b)=sup{s:s|a $ and $ s|b}=gcd(b,a)$. – user52045 Nov 18 '13 at 21:55
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How to start, What is there to be shown?
I imagine that you are going through an exercise: you have an idea that you have some understanding about, and you are in the process of working through a rigorous development of it.
Typically, these things start with some sort of precise definition. You'll have to consult your book/notes to know what that is. But two typical ways to begin are as follows:
$\gcd(a,b)$ is defined to be a nonnegative integer $c$ with the property that, whenever an integer $d$ divides both $a$ and $b$, then $d$ also divides $c$.
or
$\gcd(a,b)$ is the smallest positive number you can create by computing $ma + nb$, where $m,n$ are integers, or $0$ if $a=b=0$.
In both cases, if you swap $a$ and $b$, you get something different. Although, it is something different that is very easy to show is equivalent to the original. Your book/notes are likely to be very similar to this.