We propose an alternative method to factorize an integer by using three harmonic oscillators. These oscillators are coupled together via specific Kerr nonlinear interactions. This method can be applied even if two harmonic oscillators are prepared in mixed states. As simple examples, we show how to factorize N=15 and 35 using this approach. The effect of dissipation of the harmonic oscillators on the performance of this method is studied. We also study the realization of nonlinear interactions between the coupled oscillators. However, the probability of finding the factors of a number is inversely proportional to its input size. The probability becomes low when this number is large. We discuss the limitations of this approach.