No, She is not correct.
Explanation:
To find the greatest common factor of the expression 20x + 100xy. 
Given expression 20x + 100xy. 
Let us factor the expression 20x + 100xy. 
Now take the common factor in the expression 20x + 100xy. 
The common factor is 20x. 
So, 20x + 100xy = 20x( 1+ 5y) 
But Claudia says that the greatest common factor is 20(x+5xy). 
The GCF is wrong. 
So, she is not correct.