The clotting factor in plasma is fibrinogen but we do not have clots in our blood vessels as we have a natural anticoagulant called:
Heparin
Anticoagulants are chemical substances that prevent or reduce coagulation of blood, prolonging the clotting time. Heparin is the natural anticoagulant present in our body. For blood-related disorders, anticoagulants are used in therapy.