Question

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hat is the greatest common factor of 2x^2 and 4x^2y ?

Answer 1

To find the greatest common factor (GCF) of the two terms \(2x^2\) and \(4x^2y\), we need to identify the common factors in both terms.

1. **Identify the coefficients**:
- The coefficients are \(2\) and \(4\).
- The GCF of \(2\) and \(4\) is \(2\).

2. **Identify the variable factors**:
- Both terms have \(x^2\) as a factor.
- The GCF of \(x^2\) and \(x^2\) is \(x^2\).

3. **Look at the variable \(y\)**:
- The first term \(2x^2\) does not have \(y\) as a factor, while the second term \(4x^2y\) does. Therefore, \(y\) is not a common factor.

Now we can combine the GCF of the coefficients and the variable parts:

\[
\text{GCF} = 2 \cdot x^2 = 2x^2
\]

Thus, the greatest common factor of \(2x^2\) and \(4x^2y\) is \(2x^2\).