hello there! My grandmother has become very ill and my mother has been staying with her and helping my grandmother straighten out her affairs. I received this cutting in the mail as a gift, unfortunately she has been struggling with her memory and couldn't remember the name of this cactus, she said she thinks she got it from arizona but I'm not too sure how reliable that information is. The main plant was in between 5-6ft tall before this piece was cut off the top. I'm still kind of a beginner and appreciate any help!

here are some photos: