Question

How do you find the gcf of `6a + 18a^2`?

Answer 1

Prime factors:
`color(white)("XXXX")` `6a = color(blue)(2)xxcolor(blue)(3)xxcolor(blue)(a)`
`color(white)("XXXX")` `18a^2 =color(blue)(2)xxcolor(blue)(3)xx3xxcolor(blue)(a)xxa`

Select pairs of identical terms from each factoring:
`color(white)("XXXX")` `2xx3xxa = 6a`

The greatest common factor (gcf) of `6a` and `18a^2` is
`color(white)("XXXX")` `6a`.

(...and, yes, you could have simply recognized that `(6a)` is a factor of `(18a^2)` but it is probably better to see how this should be handled in the general case.)