Answer:
9
Step-by-step explanation:
the easiest way is the Euclid's algorithm
[tex]36=27(1)+9\\\\27=9(3)+0[/tex]
so 9 is the GCF
if you don't know the Euclid's algorithm
we first need to factorize 27 and 36
[tex]27=3*9=3*3*3=3^{3}[/tex]
[tex]36=2*18=2*2*9=2*2*3*3=2^{2}*3^{2}[/tex]
and the common factor is 3
and the highest common exponent is 2 (of the factor 3)
so the GCF=[tex]3^{2} =9[/tex]
as you can see it's easier the Euclid's algorithm
