Order of reactivity of HX towards Alcohols is

Reactivity of HX depends on nucleophilicity of halide ion, Nucleophilicity order:${\mathrm{I}}^{-}>{\mathrm{Br}}^{-}>{\mathrm{Cl}}^{-}>{\mathrm{F}}^{-}$ . In other words we can also say that HI is the strongest acid and reacts most.

Hence the reactivity order is HI>HBr>HCl>HF