A differential device differentially distributes a driving force to first and second axles. The differential device is comprised of a differential gear set configured to allow differential motion between the first and second axles, a casing rotatable about an axis, the casing housing and being drivingly coupled with the differential gear set and including a first end wall, a second end wall axially opposed to the first end wall, and a side wall disposed radially outward, which in combination with the first end wall and the second end wall defines a chamber configured to house the differential gear set, a clutch engageable with the differential gear set, a solenoid configured to drive the clutch, which is disposed adjacent to the first end wall, and a magnetic core fixed to the solenoid. The magnetic core is comprised of a sleeve portion snugly and slidably fitting around an outer periphery of the side wall to radially position the core and the solenoid in place.