Which is the largest number that will divide 2036 and 233 leaving remainders 12 and 13, respectively?

The number divides 2036 and 233 leaves the remainder 12 and 13 respectively.

So, The number will divide (2036 - 12) and (233 - 13) completely.

Now, The Largest number that will divide 2024 and 220 completely will be the HCF of these numbers.

2024 = $$44\times\ 46$$

220 = $$44\times\ 5$$

So, 44 is the HCF and the number which will divides 2036 and 233 leaves the remainder 12 and 13 respectively.

Hence, Option B is correct.