Is the Avogadro constant used in the Avogadro's law formula?

The mathematical expression for Avogadro's law is

#"V"/"n" = "constant"#, where

#V# - the volume of the ideal gas;
#n# - the amount of gas - expressed in moles;

So, what that above equation suggests is that there is a relationship between the volume a gas occupies and how much of that gas is present; this takes place for constant temperature and constant pressure, which, using the ideal gas law, implies that

#PV = nRT => V = (nRT)/P => V/n = (RT)/P = "constant"#, since

#R#, #P#, and #T# are all constants in this case.

To answer your question, Avogadro's number is not used in the formula for Avogadro's law; however, it could be, if you take into account the fact that

#N = n*N_A#, where

#N# - the number of molecules of gas present;
#n# - the number of moles of gas;
#N_A# - Avogadro's number - #6.022*10^(23)# #"molecules/mol"#

If you multiply the ideal gas equation by #N_A/N_A# on the right-hand side, you'll get

#PV = n*N_A/N_A *RT = n*N_A * R/N_A * T = N * R/N_A * T#,

where #R/N_A = k# - Boltzmann's constant = #1.38*10^(-23)# #"J/K"#

So, in this form, #PV = NkT#, so you could write Avogadro's law using

#V/N = (kT)/P = "constant"#