Monte Carlo (MC) codes can be computationally expensive for core neutronics analyses and prohibitive in transient simulations. MC codes can also be used to generate few-group homogenized constants. These are then used by nodal diffusion codes, which offer time-efficient few-group nodal solutions. To ensure that the MC solution is reproduced by the diffusion solver, reference discontinuity factors (DFs) are required. This paper uses the Jacobian-Free Newton Krylov (JFNK) iterative scheme to generate the few-group DF values. The primary objective is to verify the JFNK-generated DFs against the nodal expansion method (NEM) semi-analytical solution. Multiple verification cases, ranging from a 1D multi-nodal problem to a 2D small modular reactor (SMR) core, are used to compare the DFs values and the corresponding flux solutions. The homogenous flux solutions obtained by the nodal diffusion code, DYN3D, yield near perfect agreement with the reference power profiles only when complemented by the generated correction DFs.