Question

What is the greatest common factor of `28u^10v^6,36u^6v^5, and 49u^5v`?

Answer 1

`7u^5v`

Explanation:

Separating each component of `color(red)(28u^10v^6),color(blue)(36u^6v^5),color(green)(49u^5v)`:

#{: (,"||",color(red)(28),color(blue)(35),color(green)(49),"||",color(red)(u^10),color(blue)(u^6),color(green)(u^5),"||",color(red)(v^6),color(blue)(v^5),color(green)(v)), ("Factors: ","||",color(red)(2xx2xx7),color(blue)(5xx7),color(green)(7xx7),"||",color(red)(u^5xxu^5),color(blue)(u^5xxu),color(green)(u^5),"||",color(red)(vxxv^5),color(blue)(vxxv^4),color(green)(v)), (GCF,"||",,7,,"||",,u^5,,"||",,v,) :}#

Recombining the GCF of the components:
`color(white)("XXX")color(magenta)(7u^5v`