Question
Find the greatest common factor.'
9z^3,6z^3
9z^3,6z^3
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the terms \(9z^3\) and \(6z^3\), we can proceed with the following steps:
1. **Find the GCF of the coefficients**:
- The coefficients are 9 and 6. The factors of 9 are \(1, 3, 9\) and the factors of 6 are \(1, 2, 3, 6\). The greatest common factor of 9 and 6 is \(3\).
2. **Find the GCF of the variable part**:
- Both terms have \(z^3\). The GCF of \(z^3\) and \(z^3\) is \(z^3\).
3. **Combine the GCF of the coefficients and the variable part**:
- Therefore, we multiply the GCF of the coefficients by the GCF of the variable parts:
\[
\text{GCF} = 3 \cdot z^3 = 3z^3.
\]
Thus, the greatest common factor of \(9z^3\) and \(6z^3\) is \(\boxed{3z^3}\).
1. **Find the GCF of the coefficients**:
- The coefficients are 9 and 6. The factors of 9 are \(1, 3, 9\) and the factors of 6 are \(1, 2, 3, 6\). The greatest common factor of 9 and 6 is \(3\).
2. **Find the GCF of the variable part**:
- Both terms have \(z^3\). The GCF of \(z^3\) and \(z^3\) is \(z^3\).
3. **Combine the GCF of the coefficients and the variable part**:
- Therefore, we multiply the GCF of the coefficients by the GCF of the variable parts:
\[
\text{GCF} = 3 \cdot z^3 = 3z^3.
\]
Thus, the greatest common factor of \(9z^3\) and \(6z^3\) is \(\boxed{3z^3}\).