How do you find the greatest common factor of #36xy^3, 24y^2#?

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Answer 1 · 2016-12-11T14:16:53

#12y^2#

#color(blue)("Consider the variables "x" and "y) #

#x# is only in one of them so it is not 'common'. Thus it is not included in the GCF

#y^2xxy=y^3# so #color(green)(y^2" is part of the GCF")#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider the coefficients 36 and 24")#

Using prime factors: If you have any doubts at all sketch a factor tree.
Tony B

From this observe that the 'common' prime factors are

#color(green)(2xx2xx3 =12" is part of the GCF")#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

GCF #-> 12y^2#