In the first century before Christ, the Pythagorean school, considered THREE a perfect number, since synthesis of the even (two) and the odd (one).
For the Chinese THREE is perfect because it is the number of cosmic entirety: heaven, earth, human being.
Divine triads are frequent in religions, from the Hindu Trimurti (Brahma, Shiva, Vishnu) to the Trinity of Christianity.
In the Middle Ages, in the Divine Comedy of Dante, THREE and its multiples have a symbolic value (three parts, thirty-three cantiche, nine infernal circles).
To me THREE is simply magic, it always fits like a glove.