An iterative technique is displayed whereby factors of arbitrary degree can be found for polynomials in one variable. Convergence is shown to occur always if a certain Jacobian does not vanish and if the initial approximation to a factor is near enough to an actual factor. The process is simply programmed, and preliminary results indicate it to be well adapted to use with digital computers. For factors of degree two, the technique is similar to that of Bairstow, the present method being somewhat simpler.