The "purpose" of a remainder, if any, will depend upon the context. But I believe that usually, yes, the point is that the divisor is not a factor of the dividend.
I was not sure to put it here or in the pre-calc im sorry if it is in the incorrect location.
when I do polynomial long division I sometimes have a remainder, does this remainder have any other purpose other then telling us that the numbers do not go evenly into one another.
Thanks