10. (10 points) Teacher Guo has a cake to share with 4 or 5 children, so Teacher Guo cuts the cake into several pieces, which may not be of the same size; in this way, whether 4 or 5 children come, they can take some pieces so that each person gets the same amount. Therefore, Teacher Guo must cut the cake into at least $\qquad$ pieces.
【Answer】Solution: According to the problem, cut the cake three times, one cut each horizontally, vertically, and longitudinally, the four large pieces each occupy $\frac{1}{5}$, the sum of the four small pieces occupies $\frac{1}{5}$, answer: Teacher Guo divides the cake into at least 8 pieces.

Therefore, the answer is 8.