There cannot be a common factor of just one number. To be common there need to be at least two numbers. If you find all the factors of two or more numbers, and you find some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
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Since 27 is a factor of 54, and 27 cannot have a larger factor than itself, the greatest common factor of 27 and 54 is 27.
The greatest common factor of 27 and 36 is 9.
The greatest common factor of 14 and 27 is 1.
The Greatest Common Factor of 18, 27, and 30 is 3.
Since 27 is a factor of 81, it is automatically the GCF.It is: 27