Question

The greatest common factor of 45a^2b^3 and 18a^4b

Answer 1

9a²b

Explanation:

Hi there!

We need to find the greatest common factor out of 45a²b³ and 18
`a^(4)`b

We can split apart the monomials to make it easier

45a²b³ is 45*a²b³

18
`a^(4)`b is 18*
`a^(4)`b

First, let's find the GCF out of 45 and 18 (the number coefficients)

we can find all of the multiples of the 2 numbers:

45 is made up of 9 and 5

9 is made up of 3 and 3

so 3*3*5 is 45

18 is made up of 2 and 9

9 is made up of 3 and 3

so 2*3*3 is 18

3*3 is in both 45 and 18, so 9 is the GCF out of 45 and 18

Now let's find the GCF out of a²b³ and
`a^(4)`b

a²b³ made up of a² and b³

so a²b³ is a*a*b*b*b

`a^(4)`b is made up of
`a^(4)` and b

so
`a^(4)`b is a*a*a*a*b

a*a*b is in both a²b³ and
`a^(4)`b, so the GCF out of a²b³ and
`a^(4)`b is a²b

Now multiply 9 and a²b together, as they are only the GCF of the parts of the monomials

9*a²b=9a²b

there's the greatest common factor of the 2 monomials

Hope this helps!