High-statistics measurements of differential cross sections and recoil polarizations for the reaction γp → K + 0 have been obtained using the CLAS detector at Jefferson Lab. We cover center-of-mass energies ( √ s) from 1.69 to 2.84 GeV, with an extensive coverage in the K + production angle. Independent measurements were made using the K + pπ − (γ ) and K + p(π − , γ ) final-state topologies, and were found to exhibit good agreement. Our differential cross sections show good agreement with earlier CLAS, SAPHIR, and LEPS results, while offering better statistical precision and a 300-MeV increase in √ s coverage. Above √ s ≈ 2.5 GeV, tand u-channel Regge scaling behavior can be seen at forward and backward angles, respectively. Our recoil polarization (P ) measurements represent a substantial increase in kinematic coverage and enhanced precision over previous world data. At forward angles, we find that P is of the same order of magnitude but opposite sign as P , in agreement with the static SU(6) quark model prediction of P ≈ −P . This expectation is violated in some mid-and backward-angle kinematic regimes, where P and P are of similar magnitudes but also have the same signs. In conjunction with several other meson photoproduction results recently published by CLAS, the present data will help constrain the partial-wave analyses being performed to search for missing baryon resonances.