**Core Concept**
Factor II (prothrombin) is a crucial coagulation protein that participates in the extrinsic and common coagulation pathways. Both activated partial thromboplastin time (APTT) and prothrombin time (PT) measure the integrity of the coagulation cascade. A deficiency in Factor II would affect both pathways, leading to prolonged APTT and PT.

**Why the Correct Answer is Right**
In Factor II deficiency, the coagulation cascade is impaired because of the lack of prothrombin, which is essential for the conversion of fibrinogen to fibrin. This deficiency affects both the extrinsic pathway (measured by PT) and the common pathway (measured by APTT), resulting in prolonged times for both tests. The Factor II deficiency disrupts the conversion of prothrombin to thrombin, leading to an accumulation of prothrombin in the plasma and a subsequent prolongation of both PT and APTT.

**Why Each Wrong Option is Incorrect**
**Option A:** Factor XIII deficiency would primarily affect the stability of the fibrin clot, which would not necessarily prolong PT or APTT. Factor XIII deficiency would rather lead to a prolongation of the bleeding time or a clot lysis time.
**Option B:** Heparin administration would actually prolong APTT by inhibiting the coagulation cascade, but it would not affect PT, which measures the extrinsic pathway.
**Option C:** Thrombocytopenia would primarily affect the platelet count and function, leading to impaired primary hemostasis and a prolonged bleeding time, but not necessarily affecting PT or APTT.

**Clinical Pearl / High-Yield Fact**
In cases of suspected coagulopathy, it's essential to remember that both PT and APTT can be prolonged in conditions affecting the common pathway, such as Factor II deficiency. This can help guide further evaluation and treatment.

**✓ Correct Answer: A. Factor II deficiency**