No. 26 and 65 both have a common factor of 13, since 26 = 2•13 and 65 = 5•13, so GCD(26, 65) = 13 ≠ 1.
We can also arrive at this using Euclid's algorithm.
65 = 58 + 7 = 2•26 + 13
26 = 2•13 + 0
Since the last remainder is zero, the previous remainder is the GCD.