Question

Identify the greatest common factor of 12a^4b^7 and 18a^5b^3

Answer 1

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

1. **Find the GCF of the 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 common factors are \(1, 2, 3, 6\).
- Therefore, the GCF of 12 and 18 is **6**.

2. **Find the GCF of the variables \(a^4\) and \(a^5\)**:
- The GCF for \(a^n\) terms is \(a^{\min(m,n)}\).
- Here, \(m = 4\) and \(n = 5\), so \(\min(4, 5) = 4\).
- Thus, the GCF of \(a^4\) and \(a^5\) is \(a^4\).

3. **Find the GCF of the variables \(b^7\) and \(b^3\)**:
- Again, we use \(b^{\min(m,n)}\).
- Here, \(m = 7\) and \(n = 3\), so \(\min(7, 3) = 3\).
- Therefore, the GCF of \(b^7\) and \(b^3\) is \(b^3\).

4. **Combine the GCFs**:
- Putting it all together, we have:
\[
\text{GCF} = 6a^4b^3
\]

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