[amp_mcq option1=”26, 78″ option2=”13, 156″ option3=”36, 68″ option4=”39,52″ correct=”option1″]
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.