Refer to figure.
apparent wander → INCORRECT.  This refers to the apparent change of gyro orientation due to the rotation of the Earth or transport across its curved surface.

the number of gimbals used to support the gyro → INCORRECT.  Gimbals give gyroscopes degrees of freedom to maintain their orientation, they have no effect on rigidity.

the precessional force → INCORRECT.  Precession is the response of a gyro to an unbalanced torque around an axis other than its spin axis, it has no effect on rigidity.

the mass and speed of rotation → CORRECT.  These are the major factors affecting rigidity.

A rotating mass, such as a gyroscope, will tend to resist changes to its orientation in space.  This is known as gyroscopic rigidity, the more rigid it is the less it will respond to an unbalanced torque and vice versa.  This property is very useful in instruments which need a reference datum such as an attitude indicator or directional gyro.

Factors affecting rigidity:

• Speed of rotation - the faster it spins the more rigid it is.
• Mass - the greater the mass of the rotor the more rigid it will be.
• Distribution of Mass - the further the mass is from the axis of rotation the greater the rigidity.