In this paper, we present an algorithm to factor a differential operator L = σn + cn 1σn-1 + ··· + c1σ+c0 with coefficients ci in C{y}, where C is a constant field and C{y} is the ordinary differential polynomial ring over C. Also, we discuss the applications of the algorithm in decomposing nonlinear differential polynomials and factoring differential operators with coefficients in the extension field of C.