Searches are presented for heavy gauge bosons decaying into a top and a bottom quark in data collected by the CMS experiment at sqrt(s) = 13 TeV that correspond to an integrated luminosity of 2.2 and 2.6 inverse femtobarns in the leptonic and hadronic analyses, respectively. Two final states are analyzed, one containing a single electron, or muon, and missing transverse momentum, and the other containing multiple jets and no electrons or muons. No evidence is found for a right-handed W' boson (W'[R]) and the combined analyses exclude at 95% confidence level W'[R] with masses below 2.4 TeV if M[W'[R]] >> M[nu[R]] (mass of the right-handed neutrino), and below 2.6 TeV if M[W'[R]] < M[nu[R]]. The results provide the most stringent limits for right-handed W' bosons in the top and bottom quark decay channel.