Question
Find the greatest common factor.'
6z,3z^2
6z,3z^2
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the expressions \(6z\) and \(3z^2\), we can follow these steps:
1. **Factor the coefficients**:
- The coefficient of \(6z\) is \(6\).
- The coefficient of \(3z^2\) is \(3\).
- The GCF of \(6\) and \(3\) is \(3\).
2. **Factor the variables**:
- The variable part of \(6z\) is \(z\).
- The variable part of \(3z^2\) is \(z^2\).
- The GCF of \(z\) and \(z^2\) is \(z\) (since the lowest power of \(z\) is \(z^1\)).
3. **Combine the GCF of the coefficients and the variables**:
- The GCF of \(6z\) and \(3z^2\) is \(3z\).
Thus, the greatest common factor of \(6z\) and \(3z^2\) is \(\boxed{3z}\).
1. **Factor the coefficients**:
- The coefficient of \(6z\) is \(6\).
- The coefficient of \(3z^2\) is \(3\).
- The GCF of \(6\) and \(3\) is \(3\).
2. **Factor the variables**:
- The variable part of \(6z\) is \(z\).
- The variable part of \(3z^2\) is \(z^2\).
- The GCF of \(z\) and \(z^2\) is \(z\) (since the lowest power of \(z\) is \(z^1\)).
3. **Combine the GCF of the coefficients and the variables**:
- The GCF of \(6z\) and \(3z^2\) is \(3z\).
Thus, the greatest common factor of \(6z\) and \(3z^2\) is \(\boxed{3z}\).