Final answer:
The liver is responsible for synthesizing many of the coagulation factors, using vitamin K to produce essential components for the clotting process, reflected in coagulation tests like the INR.
Step-by-step explanation:
The organ responsible for the synthesis of many of the coagulation factors is the liver. The liver produces essential clotting factors which include fibrinogen (factor I), prothrombin (factor II), and factors V, VII, IX, X, and XI. Additionally, it synthesizes protein C, protein S, and antithrombin which play a crucial role in the coagulation process. Vitamin K, essential for the production of several clotting factors, is utilized by the liver and is also synthesized by bacteria in the large intestine.
Coagulation tests such as the international normalized ratio (INR) are used to measure the efficiency of blood clotting and reflect the liver's production of these factors.