We ask for simple controllers to stabilize linear systems. Thereby, we focus on what we call separable controllers, i.e., controllers which can be factorized into a Kronecker product of two smaller matrices. It is shown that a certain class of linear systems can be stabilized by such controllers. Consequently, the complexity of separable controllers, quantified in terms of the number of variables required to represent the controller, say on a computer, is minimized. The latter yields number theoretic insights into our problem.