Step 1: Decode the name. The disorder is literally called Factor V Leiden thrombophilia, naming both the factor involved and the city where it was described, and it is the commonest inherited clotting tendency.
Step 2: State the genetic defect. It results from a single mutation in the $Factor\ V$ gene that alters the protein.
Step 3: Trace the consequence. The altered Factor V cannot be cleaved and inactivated by activated protein C, removing a natural brake on coagulation and leaving the patient prone to abnormal venous clots.
Step 4: Rule out the rest. None of Factor VII, IX, or X is implicated in this entity, so the answer must be Factor V.
\[\boxed{\text{Factor V}}\]