The factors of 125 are:
1, 5, 25, 125
The factors of 450 are:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The common factors are: 1, 5, 25
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There cannot be a greatest common factor (GCF) 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.
250, 500, 750, 1000, 1250, 1500, 1750, 2000, 2250, 2500 . . .
300 150,2 75,2,2 25,3,2,2 5,5,3,2,2 750 375,2 125,3,2 25,5,3,2 5,5,5,3,2 2 x 3 x 5 x 5 = 150, the GCF.
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The GCF is 10.