Final answer:
The liver is primarily responsible for producing clotting factors necessary for blood coagulation, relying on vitamin K to do so.
Step-by-step explanation:
The organ associated with the production of the majority of clotting factors is the liver. The liver produces coagulation factors I (fibrinogen), II (prothrombin), V, VII, IX, X, XI, protein C, protein S, and antithrombin. These clotting factors are essential for the blood's ability to clot and prevent excessive bleeding. The liver's production of clotting factors is dependent on the fat-soluble vitamin K, which is consumed in the diet and synthesized by bacteria in the large intestine.