Identify the greatest common factor of 12a4b7 and 18a5b3 .(1 point) Responses 12a4b3 12 a superscript 4 baseline b superscript 3 baseline 6a4b3 6 a superscript 4 baseline b superscript 3 baseline 12a5b7 12 a superscript 5 baseline b superscript 7 baseline 6a5b7

Answer 1

To find the greatest common factor (GCF) of the expressions \(12a^4b^7\) and \(18a^5b^3\), we need to factor both coefficients and the variables separately.

1. Coefficients:

   • 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 GCF of \(12\) and \(18\) is \(6\).

2. Variable \(a\):

   • For \(a^4\) and \(a^5\), the GCF is \(a^{\text{min}(4,5)} = a^4\).

3. Variable \(b\):

   • For \(b^7\) and \(b^3\), the GCF is \(b^{\text{min}(7,3)} = b^3\).

Now we combine the results:

\[ \text{GCF} = 6a^4b^3 \]

Thus, the greatest common factor of \(12a^4b^7\) and \(18a^5b^3\) is \(6a^4b^3\).

The correct response is \(6a^4b^3\).