Given two linearly independent matrices in so(3), Z(1) and Z(2), every rotation matrix, X-f is an element of SO(3), can be written as the product of alternate elements from the one-dimensional subgroups corresponding to Z(1) and Z(2), namely X-f = e(Z1t1)e(Z2t2)e(Z1t3 . . .) e(Z1ts). The parameters t(i), i = 1,..., s are called Generalized Euler Angles. In this paper, the minimum number of factors required for the factorization of X-f is an element of SO(3), as a function of X-f, is evaluated. An algorithm is given to determine the generalized Euler angles, in the optimal factorization. The results can be applied to the bang-bang control, with minimum number of switches, of some classical and quantum systems. (C) 2004 Elsevier Ltd. All rights reserved.