Question

Linear Expressions, Equations & Inequalities Online Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
What is the greatest common factor of 12a2b3
and 18a3b
?(1 point)
Responses

6ab2
6 a b superscript 2 baseline

6a2b
6 a superscript 2 baseline b

12a5b4
12 a superscript 5 baseline b superscript 4 baseline

12a2b

Answer 1

To find the greatest common factor (GCF) of the expressions \(12a^2b^3\) and \(18a^3b\), we need to consider the numerical coefficients and the variables separately.

1. **Numerical 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 Factors:**
- For \(a\): \(a^2\) and \(a^3\) → the lower power is \(a^2\).
- For \(b\): \(b^3\) and \(b\) → the lower power is \(b\).

Combining these factors, the GCF is:
\[
6a^2b
\]

Thus, the answer is:
**6a²b** (which corresponds to "6 a superscript 2 baseline b").