The location of {gamma}-ray-emitting region in blazars has been an open issue for several decades and is still being debated. We use the Paliya et al. sample of 619 {gamma}-ray-loud flat-spectrum radio quasars with available spectral energy distributions and employ a seed photon factor approach to locate the {gamma}-ray production region. This method efficiently sets up a relation between the peak frequencies and luminosities for the synchrotron emission and inverse Compton scattering, together with a combination of the energy density and characteristic energy for the external seed photon field, namely, sqrt{U_0_}/{epsilon}_0_, an indicative factor of seed photons in units of Gauss. By comparing it with canonical values of the broad-line region (BLR) and molecular dusty torus (DT), we principally ascertain that the GeV emission originated far beyond the BLR and close to the DT-farther out at parsec scales from the central black hole, which supports a far-site scenario for {gamma}-ray blazars. We probe the idea that inverse Compton scattering of infrared seed photons is happening in the Thomson regime. This approach and our findings are based on the validity of the external Compton model, which is applicable in understanding the GeV emission mechanism in FSRQs. However, the completeness of this framework has been challenged by reports of neutrino emission from blazars. Thus, we also shed new light on the neutrino production region by using our derived results because blazars are promising neutrino emitters.