Theoretical and experimental studies present that metal halogens in MX3 forms can show very interesting electronic and magnetic properties in their bulk and monolayer phases. Many MX3 materials have layered structures in their bulk phases, while RuBr3 and RuI3 have one-dimensional chains in plane. In this paper, we show that these metal halogens can also form two-dimensional layered structures in the bulk phase similar to other metal halogens, and cleavage energy values confirm that the monolayers of RuX3 can be possible to be synthesised. We also find that monolayers of RuX3 prefer ferromagnetic spin orientation in the plane for Ru atoms. Their ferromagnetic ground state, however, changes to antiferromagnetic zigzag state after U is included. Calculations using PBE+U with SOC predict indirect band gap of 0.70 eV and 0.32 eV for the optimized structure of RuBr3 and RuI3, respectively. Calculation based on the Monte Carlo simulations reveal interesting magnetic properties of RuBr3, such as large Curie temperature against RuI3, both in bulk and monolayer cases. Moreover, as a result of varying exchange couplings between neighboring magnetic moments, magnetic properties of RuBr3 and RuI3 can undergo drastic changes from bulk to monolayer. We hope our findings can be useful to attempt to fabricate the bulk and monolayer of RuBr3 and RuI3.