If you watched dragon, look at finger.
Dragon (snake shape) is imaginary animal in East Asia.
Dragon was the symbol of Chinese Emperor, it never allowed using this design by others including nations around China.
That is to say, China was the center for all things.
Accordingly, the Emperors of nations around China were sensitive to this, they settled that reducing the number of claws.
China : five claws (five fingers).
Korea : four claws (four fingers).
Japan : three claws (three fingers).
Of course, it have nothing to do with that at present, because Chinese Emperor had gone. (This tradition a little remains now.)