This paper reports a detailed study of generalized Chaplygin gas (GCG) with power law form of scale factor and truncated form of the scale factor using binomial expansion in both interacting and non-interacting scenarios along with its cosmological consequences, studied in terms of equation of state (EoS) parameter. In the non-interacting scenario, the EoS parameter behaves as quintessence in both forms of the scale factor. In the interacting scenario, the EoS parameter behaves as phantom and for the truncated form of the scale factor, it violates the constraints of the positive parameter α. The cosmological implementation of GCG interacting with pressureless dark matter is investigated in the framework of f(T) modified gravity, where T is the torsion scalar in teleparallelism. The interaction term is directly proportional to the GCG density with positive coupling constant. In f(T) gravity, the EoS is behaving like phantom. The stability of the reconstructed model is investigated and it is found to be stable against small gravitational perturbations, i.e., the squared speed of sound is non-negative and an increasing function of cosmic time t. We have observed that our reconstructed f(T) model satisfies one of the sufficient conditions of a realistic reconstructed model and it is consistent with the CMB constraints and primordial nucleosynthesis. Cosmology of primordial perturbations has also been analyzed and the self-interacting potential has been found to be an increasing function of cosmic time t.