Answer:
In 1964 it was decided that the Electoral College would consist of 538 members since that is the number of congressmen that the Federal Congress has, that is, the sum of senators and representatives in the national Legislative Power is 538.
Therefore, given that each state has the same representation in the Electoral College as it has in Congress, and that Congress has that number of congressmen, the number of 538 electors for the Electoral College was set.