A clutch device is combinable with a rotating device rotating about an axis. The clutch device is provided with a clutch rotatable with the rotating device, a plunger for disengageably engage the clutch, a solenoid for generating a magnetic flux for driving the plunger, a magnetic core slidably fitting on a portion of the rotating device and incompletely enclosing the solenoid to expose the solenoid to the portion, and a support member configured to support the magnetic core to fit with the rotating device in an axial direction along the axis. The magnetic core in combination with the portion of the rotating device and the plunger is so dimensioned as to enclose the solenoid.