As the name suggests, the greatest common factor of two numbers is the largest number that divides both numbers. So, the first two options are surely wrong: 9 can't be the GCF of 9 and 12 because it doesn't divide 12, and it can't be the GCF of 9 and 30 because it doesn't divide 30.
As for the third option, 18 and 36 are actually both multiples of 9, but 9 isn't the GCF, because both numers are divisible by 18. So, the greatest common factor between 18 and 36 is 18 itself.
So, the answer is the last option, because you have
[tex] 18 = 9\cdot 2,\quad 27 = 9\cdot 3 [/tex]
So, 9 is actually the greatest common factor between 18 and 27.
