How do you find the GCF of #60r^2, 45r^3#?

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Answer 1 · 2017-04-25T15:42:30

#15r^2#

First, let's identify the factors of #60# and #45#

For #60# we have...

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

and for #45# we have

1, 3, 5, 9, 15, 45

For our Greatest Common Factor or GCF, we need to find the biggest number that is a factor of both #60# and #45#

In this case that is #15#

60 = 1, 2, 3, 4, 5, 6, 10, 12, #color(red)15#, 20, 30, 60

45 = 1, 3, 5, 9, #color(red)15#, 45

So now we can say we have

#color(red)15r^2# and #color(red)15r^3#

but remember that we can simplify the exponents of the variables as well.

We have #r^2# and #r^3#

What is the largest exponent that these two have in common?
Think of it like this...

#r^2# is #r# and #r^2#

#r^3# is #r#, #r^2# and #r^3#

See how we count up to find the exponent of greatest power
So, now we can see that the GCF for the #r# is #r^2#

#r^2# is #r# and #color(green)(r^2)#

#r^3# is #r#, #color(green)(r^2)# and #r^3#

So now we know that our GCF is:

#color(red)15color(green)(r^2)#