1 and 13
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There can be no greatest common denominator. Suppose x is the greatest common denominator. That requires that 39 divides x, 26 divides x and x is the greatest such number. But 39 will divide 2x and 26 will divide 2x and 2x is greater than x. So x could not have been a GCD.
13.
The factors of 39 are - 1, 3, 13, and 39 So, each can be divided evenly into 39. The prime factors are 3 and 13.
2, 26, 39
13 does.