What is the gcd of 39 and 26?

Answer 1

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.