It seems to have been accomplished with relative ease, with the Roman Empire bringing to an end the "Ancient Greece" that had lasted for so long. Was it simply numbers, technology or the fact that the Greeks couldn't get along enough to unite again against a common foe?
The political disunity amongst the Greeks: the endless struggles between the Macedonians, Achaean league, Aetolian and other cities. The Romans were able to exploit this, for instance allying with the Aetolians at first against the Macedonians and then later turning them into subject "allies" when they switched sides and were defeated.
Superior military power: proven over and over again in engagements against the Hellenistic powers. Shattering the Hellenistics phalanxes at Cynoscephalae, Pydna and Magnesia. Defeating the Greek hoplites at Corinth.