How do you find the GCF of #12y^3# and #15y^2#?

1 Answer
Oct 2, 2015

Answer:

GCF = #3y^2#

Explanation:

#{: ( , , "Factors", , , , , , , ), (12y^3 ," = ", ,2 ,xx2,xx3, ,xxy,xxy,xxy), (15y^2 ," = ", , , , color(white)("XX") 3,xx5,xxy,xxy, ), ("common factor?", , ,"N" ,color(white)("XX")"N" ,color(white)("XX")"Y" ,color(white)("XX") "N" ,color(white)("XX")"Y ", color(white)("XX")"Y",color(white)("XX")"N") :}#

The Greatest Common Factor (GCF) is the product of all the common factors:
#color(white)("XXX")3xxyxxy = 3y^2#

Note:
#color(white)("XXX")12y^3div3y^2= 4y#
#color(white)("XXX")15y^2div3y^2=5#
#4y# and #5# have no common factors, so #3y^2# is the Greatest Common Factor of #12y^3# and #15y^2#