Searches are presented for heavy gauge bosons decaying into a top and a bottom quark in data collected by the CMS experiment at root s = 13TeV that correspond to an integrated luminosity of 2.2 and 2.6 fb 1 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 2.4TeV if M-W'R >> M-vR (mass of the right-handed neutrino), and below 2.6TeV if M-W'R < M-vR. The results provide the most stringent limits for right-handed W' bosons in the top and bottom quark decay channel.