Anwer is $2$. Example: $2,2,-1,-1,0$ around a circle satisifies it. If there is an odd number, then its neighbours are even and odd. $OOE$ Also $O+O$ doesn't divide $O$ ($2$ doesn't divide an odd number) so the arrangement should be like $EOOE$. Which means we are able to pair each odd number with its unique odd neighbour. $\implies $ The sum is even. Sum can't be $1$.