Clotting factor common to extrinsic and intrinsic pathway is:

Tissue factor initiates the extrinsic pathway, whereas contact of Factor XII and platelets with collagen in the vascular wall initiates the intrinsic pathway. An especially important difference between the extrinsic  and  intrinsic  pathways is that the extrinsic  pathway can be explosive; once initiated, its speed of completion to the final clot is limited only by the amount of tissue factor released from the traumatized tissues and by the quantities of Factors X, VII,  and V in the blood. With severe tissue trauma, clotting can occur in as little as 15 seconds. The intrinsic pathway is much slower to proceed, usually requiring 1 to 6 minutes to cause clotting.  Clotting factor common to extrinsic and intrinsic pathway is Factor V.