Answer:
9a²b
Step-by-step explanation:
Hi there!
We need to find the greatest common factor out of 45a²b³ and 18[tex]a^{4}[/tex]b
We can split apart the monomials to make it easier
45a²b³ is 45*a²b³
18[tex]a^{4}[/tex]b is 18*[tex]a^{4}[/tex]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 [tex]a^{4}[/tex]b
a²b³ made up of a² and b³
so a²b³ is a*a*b*b*b
[tex]a^{4}[/tex]b is made up of [tex]a^{4}[/tex] and b
so [tex]a^{4}[/tex]b is a*a*a*a*b
a*a*b is in both a²b³ and [tex]a^{4}[/tex]b, so the GCF out of a²b³ and [tex]a^{4}[/tex]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!
