Identify the greatest common factor of 12a4b7

Question

and 18a5b3
.(1 point)
Responses

12a5b7
12 a superscript 5 baseline b superscript 7 baseline

12a4b3
12 a superscript 4 baseline b superscript 3 baseline

6a5b7
6 a superscript 5 baseline b superscript 7 baseline

6a4b3

Answer 1

To find the greatest common factor (GCF) of the two expressions \( 12a^4b^7 \) and \( 18a^5b^3 \), we can follow these steps:

1. Find the GCF of the coefficients (numerical part):

   • The coefficients are 12 and 18.
   • The factors of 12 are: 1, 2, 3, 4, 6, 12
   • The factors of 18 are: 1, 2, 3, 6, 9, 18
   • The greatest common factor of 12 and 18 is 6.

2. Find the GCF of the variables \(a\):

   • For the variable \(a\), we have \(a^4\) and \(a^5\).
   • The GCF is the lowest power, which is \(a^4\).

3. Find the GCF of the variables \(b\):

   • For the variable \(b\), we have \(b^7\) and \(b^3\).
   • The GCF is the lowest power, which is \(b^3\).

Putting it all together, the GCF of \( 12a^4b^7 \) and \( 18a^5b^3 \) is:

\[ 6a^4b^3 \]

So, the correct response is:

6a^4b^3