the GCF is the number or variables you can get out of a a term or multiple terms, when you get it out you have to be able to multiply it again and get the same terms as before for example the GCF of here is 18xy because both numbers can be divided in 18 and they both share 1 x and 1 y in common... Now divide to get your answer put the GCF outside the parenthesis and the numbers divided inside
18xy(4x + 1) if you do distributive property and multiply it you will get 72x2y+18xy see they match so the GCF of "18xy" is correct....
Hope this helped