Im looking at a homework problem I have and I am a bit confused. The first part of the question is to show that 8128 is a perfect number. This is simple enough: $1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064 = 8128$. The second part confuses me though
What is the highest power of 2 that it is factorable by? Give its cofactor. What can be said of that cofactor?
The highest power of $2$ is $2^6$, this is simple. But what is the cofactor? As far as I remember, cofactors only deal with matrices, which are not part of this problem at all. Is there some other definition I do not know about?