Question

Factor Linear Expressions Quick Check
1 of 51 of 5 Items
Question
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

6a5b7
6 a superscript 5 baseline b superscript 7 baseline

12a5b7

Answer 1

To find the greatest common factor (GCF) of the expressions \(12a^4b^7\) and \(18a^5b^3\), you can break down each term into its factors and compare them.

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 greatest common factor of 12 and 18 is **6**.

2. **Variable parts**:
- For \(a\): \(a^4\) and \(a^5\)
- The minimum power of \(a\) is \(a^4\).
- For \(b\): \(b^7\) and \(b^3\)
- The minimum power of \(b\) is \(b^3\).

3. **Combine these results**:
- The GCF is \(6a^4b^3\).

So, the correct response is:
**6a^4b^3**.