Question 4
A certain community is divided into organizations, each organization is divided into associations, each association is divided into societies and each society is divided into clubs. The number of clubs in each society, the number of societies in each association and the number of associations in each organization are the same integer which is greater than $1$. The community has a president, as does each organization, association, society and club. If there are $161$ presidential positions altogether, how many organizations are there in this community?