How phosphorus tribromide and phosphorus triiodide can form by using only two molecules of red phosphorus of bromine and iodine respectively?

Dear Student,
Chloroalkane can be formed easily with the help of PCl₃.For example when ethanol reacts with PCl₃ ,it forms chloroethane.The reaction is as follows:
3CH₃CH₂OH+PCl₃------>3CH₃CH₂Cl+H₃PO₃
But we cannot form Bromoalkane or Iodoalkane with the above method because PBr₃ and PI₃ are not stable compounds. Hence this reaction takes place in the presence of red phosphorus where this red phosphorus forms freshly prepared PBr₃ and PI₃ by reacting with bromine or iodine.

PBr₃ is prepared by treating red phosphorus with bromine. An excess of phosphorus is used in order to prevent formation of PBr₅.Equation is as follows where 2 molecules of red phosphorus is being used.
2P + 3Br₂ → 2PBr₃

Similarly PI₃ is prepared by treating red phosphorus with iodine. An excess of phosphorus is used in order to prevent formation of PI₅.Equation is as follows where 2 molecules of red phosphorus is being used.
2P + 3I₂ → 2PI₃

R--OH reacts in the presence red phosphorus/Br₂ to form R-Br(bromoalkane).
   CH₃CH₂OH+red P/Br₂------> CH₃CH₂Br
R--OH reacts in the presence red phosphorus/I₂ to form R-I(Iodoalkane).
     CH₃CH₂OH+red P/I₂------> CH₃CH₂I
R in the above examples is alkyl group

Regards