The factor that was common in the British colonization of both Australia and New Zealand was that the colonization followed Captain Cook's exploration of both areas.
Explanation:
Captain James Cook was one of the 'most famous explorers' of his times.
According to the records, he was the one to discover the continent of Australia and the 'islands of New Zealand'.
He also played an important role in disproving the theory of the existence of Terra Australias.