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.)