Banzan was born into the Motoike family in Oshinozu-mura (present-day Yonago City, Tottori Prefecture), and was adopted into the Ida family in Sainokami-mura (present-day Sakaiminato City).
大篠津村（現鳥取県米子市）の本池家に生まれ、養われて佐斐神村（現境港市）の井田家に入った。