Question
Find the greatest common factor.'
4z^3,2z
4z^3,2z
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the terms \(4z^3\) and \(2z\), we need to look at the coefficients (numerical parts) and the variable parts separately.
1. **Coefficients**: The coefficients are 4 and 2.
- The GCF of 4 and 2 is 2.
2. **Variable parts**: The variable parts are \(z^3\) and \(z\).
- The GCF of \(z^3\) and \(z\) is \(z\) (because \(z\) is the lowest power of \(z\) present in both terms).
Now, we combine the GCFs of the coefficients and the variable parts:
\[
\text{GCF} = 2z
\]
Thus, the greatest common factor of \(4z^3\) and \(2z\) is \(2z\).
1. **Coefficients**: The coefficients are 4 and 2.
- The GCF of 4 and 2 is 2.
2. **Variable parts**: The variable parts are \(z^3\) and \(z\).
- The GCF of \(z^3\) and \(z\) is \(z\) (because \(z\) is the lowest power of \(z\) present in both terms).
Now, we combine the GCFs of the coefficients and the variable parts:
\[
\text{GCF} = 2z
\]
Thus, the greatest common factor of \(4z^3\) and \(2z\) is \(2z\).