The general metric for N-dimensional spherically symmetric and conformally flat spacetimes is given, and all the homogeneous and isotropic solutions for a perfect fluid with the equation of state p = αρ are found. These solutions are then used to model the gravitational collapse of a compact ball. It is found that when the collapse has continuous self-similarity, the formation of black holes always starts with zero mass, and when the collapse has no such symmetry, the formation of black holes always starts with a mass gap.