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Apocrophon
Here what you can do is list the factors for both terms:
20: 2, 2, 5
45x: 3, 3, 5, x

The only factor that both terms share is 5, so 5 is your GCF.
Yes the GCF of 20 and 45x is 5. Due to the fact that 20: 1 & 20, 2 & 10, 4 & 5 and 45: 1 & 45, 3 & 15, 5 & 9 also only one of them has the variable x so it is not common.