We report the discovery of four transiting giant planets around K dwarfs. The planets HATS-47b, HATS-48Ab, HATS- 49b, and HATS-72b have masses of 0.369-0.021+0.031MJ, 0.243-0.030+0.022 MJ, 0.353-0.027+0.038 MJ, and 0.1254 ± 0.0039 MJ, respectively, and radii of 1.117 ± 0.014 RJ, 0.800 ± 0.015 RJ, 0.765 ± 0.013 RJ, and 0.7224 ± 0.0032 RJ, respectively. The planets orbit close to their host stars with orbital periods of 3.9228 days, 3.1317 days, 4.1480 days, and 7.3279 days, respectively. The hosts are main-sequence K dwarfs with masses of 0.674-0.012+0.016 M⊙, 0.7279 ± 0.0066 M⊙, 0.7133 ± 0.0075 M⊙, and 0.7311 ± 0.0028, and with V-band magnitudes of V = 14.829 ± 0.010, 14.35 ± 0.11, 14.998 ± 0.040 and 12.469 ± 0.010. The super-Neptune HATS-72b (a.k.a. WASP-191b and TOI 294.01) was independently identified as a transiting planet candidate by the HATSouth, WASP, and TESS surveys, and we present a combined analysis of all of the data gathered by each of these projects (and their follow-up programs). An exceptionally precise mass is measured for HATS-72b thanks to high-precision radial velocity (RV) measurements obtained with VLT/ESPRESSO, FEROS, HARPS, and Magellan/PFS. We also incorporate TESS observations of the warm Saturn-hosting systems HATS-47 (a.k.a. TOI 1073.01), HATS-48A, and HATS-49. HATS-47 was independently identified as a candidate by the TESS team, while the other two systems were not previously identified from the TESS data. The RV orbital variations are measured for these systems using Magellan/PFS. HATS-48A has a resolved 5′.4 neighbor in Gaia DR2, which is a common-proper-motion binary star companion to HATS-48A with a mass of 0.22 M⊙ and a current projected physical separation of ∼1400 au.