Find the GCF of (6x, 9x^2)

The correct answer (the GCF) is 3x.

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 3x.