disprooving factorability...?

I didn't really know what to title this thread as, but... here goes:

if a is a factor of (b + c) # proove or disprove that a is also a factor of b or a is a factor of c

Now, I'm pretty sure I understand what they are asking, and I can say without a doubt that I can disproove it, because for example, if a = 3, b = 1 c = 5. you would have, 3 is a factor of 1 + 5, or 3 is a factor of 6, which is true, however, 3 is not a factor of either 1 or 5.... I know that it is possible for that statement to be true, but the fact that I can find at least one (many more are possible, i just didn't bother after I found the first one) that disprooves it... its... disprooven right? so what I'm asking is, could I just show the example of it being false to disproove it, or is there another way I should show it?