If 2028 is the product of two natural number shaving two digits each and 13 is their highest common factor, then the numbers are

The correct answer is (a).

The prime factorization of 2028 is $2^2\cdot3\cdot13\cdot23$. The highest common factor of 2028 and 13 is 13. Therefore, the two natural numbers with two digits each and a highest common factor of 13 are 26 and 78.

The other options are incorrect because they do not have a highest common factor of 13. For example, 13 and 156 have a highest common factor of 13. However, 36 and 68 do not have a highest common factor of 13.