SOLUTION: Find the greatest common factor of the numbers or monomials. <b> 12. 9ab^2,108ab^3 Any help with this equation would be GREATLY appreciated.

Algebra ->  Equations -> SOLUTION: Find the greatest common factor of the numbers or monomials. <b> 12. 9ab^2,108ab^3 Any help with this equation would be GREATLY appreciated.      Log On


   

Question 108008: Find the greatest common factor of the numbers or monomials.

12. 9ab^2,108ab^3
Any help with this equation would be GREATLY appreciated.
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's find the numerical coefficients of the monomials.

The numerical coefficient of 9ab%5E2 is 9
The numerical coefficient of 108ab%5E3 is 108.

REMEMBER: a number is divisible by 9 if the sum of its digits is divisible by 9.

Let's check 108...

1%2B0%2B8=1%2B8=9
9 is divisible by 9. Thus, 108 is divisible by 9.

ALSO: If x is divisible by y, then their greatest common factor is x%2Fy

Thus, the greatest common factor of 108 and 9 is

108%2F9=12

Now, let's examine the variable part of the monomials

The variable part of 9ab%5E2 is ab%5E2
The variable part of 108ab%5E3 is ab%5E3

ab%5E3 is divisible by ab%5E2. So, the greatest common factor of ab%5E3 and ab%5E2 is
ab%5E3%2Fab%5E2=%28a%2Fa%29%28b%5E3%2Fb%5E2%29=1%28b%5E%283-2%29%29=b%5E1=b
Now let's MULTIPLY the two greatest common factors to get the greatest common factor of 9ab%5E2 and 108ab%5E3...

12%28b%29=12b

Therefore, the greatest common factor of 9ab%5E2 and 108ab%5E3 is 12b

Power up,
HyperBrain!