Ok, i am stuck on a problem...

I have been investigating HCF of (a,b) and noticed that a+b never seems to be a factor of the HCF (a,b).

I am not sure how i can go about proving this?

So for example, pick 2 & 3 : HCF =6 but 2+3 =5 and 5 is not a factor of 6.

This is easy to prove when the HCF (a,b) = a*b but this is not always the case?

Is it a proof by considering different cases?