We present a first-principles framework to investigate the electron scattering channels and transport properties for polar materials by combining the exact solution of the linearized electron-phonon (e-ph) Boltzmann transport equation in its integral-differential form associated with the e-ph coupling matrices obtained from the polar Wannier interpolation scheme. No ad hoc parameter is required throughout this calculation, and GaAs, a well-studied polar material, is used as an example to demonstrate this method. In this work, the long-range and short-range contributions as well as the intravalley and intervalley transitions in the e-ph interactions (EPIs) have been quantitatively addressed. Promoted by such mode-by-mode analysis, we find that in GaAs, the piezoelectric scattering is comparable to deformation-potential scattering for electron scatterings by acoustic phonons in EPI even at room temperature, and it makes a significant contribution to mobility. Furthermore, we achieved good agreement with experimental data for the mobility, and we identified that electrons with mean free paths between 130 and 210 nm provide the dominant contribution to the electron transport at 300 K. Such information provides a deeper understanding of the electron transport in GaAs, and the presented framework can be readily applied to other polar materials. ; United States. Dept. of Energy. Office of Basic Energy Sciences (Energy Frontiers Research Center. Award DE-FG02-09ER46577) ; United States. Defense Advanced Research Projects Agency. Matrerials for Transduction Program (Grant HR0011-16-2-0041)