Question

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

Answer 1

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`