How does one determine the number of core electrons an atom has?

Subtract the number of valence electrons(outer most shell electrons) from the atomic number of an atom.

Explanation: The total number of electrons for an atom equals to its atomic number. Electrons are present in different shells. Electrons present in outer most shell(valence shell) are known as valence electrons and rest of the electrons present in inner shells are known as core electrons.

So, to determine the number of electrons we subtract the valence electrons from atomic number.

For example, atomic number of N (nitrogen) is 7. It has 5 valence electrons.

Number of core electrons for N = 7 - 5 = 2

it is the most commonly accepted one