Step 1: Use the eponym as the clue. "Leiden" tags a specific mutation in factor V, discovered in the city of Leiden. So the answer is built into the name of the condition: factor V.
Step 2: Explain the mechanism. The single-base change makes factor Va resistant to inactivation by activated protein C. Protein C normally degrades factor Va to slow clotting; when it cannot, factor Va lingers, prothrombinase activity persists, and the patient drifts into a prothrombotic, clot-forming state - venous thromboembolism in particular.
Step 3: Reject the bleeders. Factor VII, IX, and X deficiencies all reduce clot formation and present with bleeding, which is the opposite of the increased clotting of factor V Leiden. They are therefore wrong.
\[\boxed{\text{Factor V}}\]