Identify the greatest common factor of 12a4b7

Question

and 18a5b3
.(1 point)
Responses

12a5b7
12 a superscript 5 baseline b superscript 7 baseline

6a4b3
6 a superscript 4 baseline b superscript 3 baseline

6a5b7
6 a superscript 5 baseline b superscript 7 baseline

12a4b3

Answer 1

To find the greatest common factor (GCF) of the expressions \(12a^4b^7\) and \(18a^5b^3\), we can break down each part.

1. Numerical Coefficients:

   • The coefficients are 12 and 18.
   • The factors of 12: \(1, 2, 3, 4, 6, 12\)
   • The factors of 18: \(1, 2, 3, 6, 9, 18\)
   • The GCF of 12 and 18 is 6.

2. Variable Parts:

   • For \(a^4\) and \(a^5\), the GCF is \(a^{\min(4, 5)} = a^4\).
   • For \(b^7\) and \(b^3\), the GCF is \(b^{\min(7, 3)} = b^3\).

Putting this all together, we have:

• GCF = \(6a^4b^3\)

Thus, the answer is: 6a4b3 (or in superscript form, \(6a^{4}b^{3}\)).