Certified GKH Gardening Expert
There are 2 plants that are referred to as Angel Trumpets, datura (flower points up) and brugmansia (flower hangs down).
Both cannot be divided in the traditional sense of the word, but daturas often reseed themselves in clumps, so there will be several plants growing in one location. These plants can be separated. Just check for multiple stems coming from the ground and each stem is a different plant.
Brugmansias are most often propagated by cuttings. They are SUPER easy to root. Here is an article on that: