Let $a,b$ be integers with $a|b$ (a divides b) and let $a>0$. Show that $(a,b)=a$. I know this is very basic, and that I'm complicating it unnecessarily, but for some reason I seem to be stuck...
Any help please?
Thanks.
Edit:
$(a,b)$ means greatest common divisor of $a$ and $b$
Answer
Well, recall the definition of $(a,b)$: it's the integer that divides both $a$ and $b$, and furthermore is the biggest integer that does so.
So how about asking:
- Does $a$ divide $a$ and $b$?
- Is $a$ the biggest integer that does so?
Hopefully this makes it obvious.
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