Let f(x,y)=0 and g(x,y)=0 be curves in R^2. Assume that the origin (0,0) is a d-fold point of f and an e-fold point of g. Let f_d(x,y) be the sum of the terms of degree d in f(x,y), g_e(x,y) be the sum of the terms of degree e in g(x,y). Then, if f_d(x,y) and g_e(x,y) have a common factor of positive degree, then the intersection multiplicity I_O(f,g)>de.