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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