The method for obtaining rational integrating factors of some rational ODEs of any order based on examination of structures of denominator and numerator of the ODEs' right-hand-side is presented. The method embodied in relatively fast procedure koif_1 can determine the explicit expression of an integrating factor under the following restriction: the denominator of integrating factor is the product of co-factors each has at least one missing independent variable. The procedure koif_2 demonstrates potential of the method without the above-mentioned restriction. The experimentations with the procedures implemented in Maple confirm consistence and efficiency of proposed method.