  The photoproduction of isolated photons, both inclusive and together with a
jet, has been measured with the ZEUS detector at HERA using an integrated
luminosity of $374\, \mathrm{pb}^{-1}$. Differential cross sections are
presented in the isolated-photon transverse-energy and pseudorapidity ranges $6
< E_T^\gamma < 15$ GeV and $-0.7 < \eta^\gamma < 0.9,$ and for jet
transverse-energy and pseudorapidity ranges $4 < E_T^{jet} < 35$ GeV and $-1.5
< \eta^{jet} < 1.8,$ for exchanged-photon virtualities $Q^2 < 1$ GeV$^2$.
Differential cross sections are also presented for inclusive isolated-photon
production as functions of the transverse energy and pseudorapidity of the
photon. Higher-order theoretical calculations are compared to the results.
