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

1 Answer
Jul 9, 2015

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.)