Well, when we're asked for a GCF, it's usually for two numbers, not two algebraic expressions. But let's see what we can do with these anyway.
What are the factors of 6x ? How about 1, 2, 3, x, 2x, 3x, and 6x ? If you divide 6x by any thing on that list, you get something else on the list, so it's actually a list of the factors of 6x .
And what are the factors of 9x² ? How about 1, 3, 9, x, 3x, 9x, x², 3x², and 9x² ? If you divide 9x² by any thing on that list, you get something else on the list, so it's actually a list of the factors of 9x² .
What are the 'common' factors ... the ones that are on both lists ?
1, 3, x, and 3x .
What's the biggest one ?
It could depend on what number 'x' is ... that's is why I have a personal problem with 'the GCF' of algebraic expressions. But as long as 'x' is any substantial number, then the biggest factor on the 'common' list is <em>3x </em>.
