Question
Find the greatest common factor.'
7z,6z^2
7z,6z^2
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the terms \(7z\) and \(6z^2\), we can break it down into two parts: the coefficients and the variables.
1. **Coefficients**: The coefficients are 7 and 6.
- The factors of 7 are 1 and 7.
- The factors of 6 are 1, 2, 3, and 6.
- The greatest common factor of 7 and 6 is 1.
2. **Variables**: The terms are \(z\) (from \(7z\)) and \(z^2\) (from \(6z^2\)).
- The common variable is \(z\).
- The lowest power of \(z\) present in both terms is \(z^1\) (or just \(z\)).
Now, we combine the greatest common factor of the coefficients and the variables:
- The GCF of the coefficients is 1.
- The GCF of the variable part is \(z\).
Thus, the greatest common factor of \(7z\) and \(6z^2\) is:
\[
\text{GCF} = 1 \cdot z = z
\]
So, the greatest common factor is \(z\).
1. **Coefficients**: The coefficients are 7 and 6.
- The factors of 7 are 1 and 7.
- The factors of 6 are 1, 2, 3, and 6.
- The greatest common factor of 7 and 6 is 1.
2. **Variables**: The terms are \(z\) (from \(7z\)) and \(z^2\) (from \(6z^2\)).
- The common variable is \(z\).
- The lowest power of \(z\) present in both terms is \(z^1\) (or just \(z\)).
Now, we combine the greatest common factor of the coefficients and the variables:
- The GCF of the coefficients is 1.
- The GCF of the variable part is \(z\).
Thus, the greatest common factor of \(7z\) and \(6z^2\) is:
\[
\text{GCF} = 1 \cdot z = z
\]
So, the greatest common factor is \(z\).