Final answer:
The liver is responsible for synthesizing various clotting factors such as fibrinogen and prothrombin, playing a key role in the coagulation process.
Step-by-step explanation:
The organ largely responsible for the synthesis of clotting factors is the Liver. The liver produces critical coagulation factors necessary for blood clotting, including factors I (fibrinogen), II (prothrombin), V, VII, IX, X, XI, protein C, protein S, and antithrombin.
It also has a vital role in storing vitamins and minerals, synthesizing proteins, and processing waste products. Vitamin K, which is essential for the production of many clotting factors, is synthesized by bacteria in the large intestine and is also necessary for the liver's function in this process.