Explanation:

- We are looking for the greatest common divisor (GCD) of 403 and 496.

- One way to find the GCD is by using the Euclidean algorithm.

- First, divide 496 by 403, then divide the remainder by the new divisor, and repeat until the remainder is zero.

- When we do this, we find the GCD is 31.

- Option 2: 31 is indeed the largest number that can exactly divide both 403 and 496.

- Option 1: 13 is not a divisor of these numbers when checked.

- Option 3: 93 is too large and not a divisor of these numbers.

- Option 4: 62 is not a common divisor of both numbers.

Green tick the answer: Option 2: 31