Problem D

Ten Slice Pizza

The DECI-Pizza Company has a special pizza that has \(10\) slices. Two of the slices are each \(\frac{1}{6}\) of the whole pizza, two are each \(\frac{1}{8}\), four are eachÂ \(\frac{1}{12}\), and two are each \(\frac{1}{24}\). A group of \(n\) friends share the pizza by distributing all of these slices. They do not cut any of the slices. Each of the \(n\) friends receives, in total, an equal fraction of the whole pizza. For what values of \(n > 1\) is this possible?