Many real-world combinatorial problems exhibit structure in the way in which their variables interact. Such structure can be exploited in the form of "factors" for representational as well as computational benefits. Factored representations are extensively used in probabilistic reasoning, constraint satisfaction, planning, and decision theory. In this paper, we formulate the factored shortest path problem (FSPP) on a collection of constraints interpreted as factors of a high-dimensional map. We show that the FSPP is not only a generalization of the regular shortest path problem but also particularly relevant to robotics. We develop factored-space heuristics for A* and prove that they are admissible and consistent. We provide experimental results on both random and handcrafted instances as well as on an example robotics domain to show that A* with factored-space heuristics outperforms A* with the Manhattan Distance heuristic in many cases.