The HCF of 4052 and 12576 will be 

Explanation -

Let's use the Euclidean algorithm:

 \(\text{Step 1: } 12576 = 4052 \times 3 + 420 \\ \text{Step 2: } 4052 = 420 \times 9 + 332 \\ \text{Step 3: } 420 = 332 \times 1 + 88 \\ \text{Step 4: } 332 = 88 \times 3 + 68 \\ \text{Step 5: } 88 = 68 \times 1 + 20 \\ \text{Step 6: } 68 = 20 \times 3 + 8 \\ \text{Step 7: } 20 = 8 \times 2 + 4 \\ \text{Step 8: } 8 = 4 \times 2 + 0 \)

The last non-zero remainder is 4.

Therefore, the HCF of 4052 and 12576 is 4.

So, the correct answer is 4.