Correct Answer - Option 3 : 13

**Concept used:**

Any number (x^{n} - 1) is divisible by (x + 1), when n is even.

**Calculation:**

Here, n = 16, which is even

(5116 - 1) is divisible by (51 + 1) = 52

And, 52 is divisible by 13.

If any number is divisible by 52 then that number is always divisible by 13

**∴ The given number (5116 - 1) is divisible by 13.**