  As a high mobility two-dimensional semiconductor with strong structural and
electronic anisotropy, atomically thin black phosphorus (BP) provides a new
playground for investigating the quantum Hall (QH) effect, including
outstanding questions such as the functional dependence of Landau level (LL)
gaps on magnetic field B, and possible anisotropic fractional QH states. Using
encapsulating few-layer BP transistors with mobility up to 55,000 cm2/Vs, we
extract LL gaps over an exceptionally wide range of B for QH states at filling
factors {\nu}=-1 to -4, which are determined to be linear in B, thus resolving
a controversy raised by its anisotropy. Furthermore, a fractional QH state at
{\nu}~ -4/3 and an additional feature at -0.56+/- 0.1 are observed,
underscoring BP as a tunable 2D platform for exploring electron interactions.
