What is the greatest common factor of 72?

There cannot be a greatest 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.
You need at least two numbers to find a GCF. If that's 7 and 2, the GCF is 1.