Question 45679
36, 54, and 180 

Write each in prime-factor form, as follows:
36= 2^2 * 3^2
54= 2 * 3^3
180 = 2^2 * 3^2 * 5

The GCF must contain the lowest prime power factors common to all the numbers:

GCF = 2 * 3^2 = 18

It doesn't have a 2^2 because 2^2 is not common to all three numbers.
It doesn't have a 3^3 for the same reason.
It doesn't have a 5 for the same reason.

Cheers,
Stan H.