Note that some of the present authors have already attempted to combine the standard time-dependent Bohmian QTM formulation with exact factorization to include quantum nuclear effects within a trajectory description of coupled electron-nuclear dynamics. Nonetheless, numerical issues associated with that study prevented the authors from en-visioning extensions to actual practical applications. Accordingly, we now present in this paper-for the first time-a proof-of-principle illustrative study that demonstrates the potential of the new scheme, and in particular, the value of combining the time-dependent interacting-trajectory-based QTM approach with exact factorization. Although only onedimensional examples are considered here, we note further that the "continuous" MIW theory adopted here (unlike the "discrete" version) readily generalizes for many-dimensional applications as well. The paper is organized as follows. Section 2 provides a brief description of the employed methodology for our quantum dynamics calculations, starting with the exact factorization formalism in Section 2.1 and continuing with the interacting quantum trajectories formalism in Section 2.2. In Section 3 we present our numerical results for various types of scattering potentials, focusing on the adiabatic case in Section 3.1 and on the nonadiabatic case in Section 3.2. We present our conclusions and perspectives in Section 4.