Question

Gcf
45x^2y^2z^2-38y^5z^3

Answer 1

What would the answer be If I have to factor the whole problem

Answer 2

To find the greatest common factor (GCF) of the expression \( 45x^2y^2z^2 - 38y^5z^3 \), we need to analyze the coefficients and the variables separately.

1. **Coefficients**:
- The coefficients are 45 and 38.
- The GCF of 45 and 38 is 1, since they do not have any common factors other than 1.

2. **Variables**:
- For \( y \), we have \( y^2 \) and \( y^5 \). The GCF is the lowest power, which is \( y^2 \).
- For \( z \), we have \( z^2 \) and \( z^3 \). The GCF is also the lowest power, which is \( z^2 \).
- The variable \( x \) only appears in the first term, so it cannot be included in the GCF.

Now we can combine these GCFs:

\[
\text{GCF} = 1 \cdot y^2 \cdot z^2 = y^2z^2
\]

Therefore, the GCF of the expression \( 45x^2y^2z^2 - 38y^5z^3 \) is:

\[
\boxed{y^2z^2}
\]

Answer 3

To factor the expression \( 45x^2y^2z^2 - 38y^5z^3 \) entirely, follow these steps:

1. **Identify the Greatest Common Factor (GCF)**:
As we found earlier, the GCF of the given expression is \( y^2z^2 \).

2. **Factor out the GCF**:
We divide each term in the expression by the GCF \( y^2z^2 \):

\[
45x^2y^2z^2 \div y^2z^2 = 45x^2
\]
\[
-38y^5z^3 \div y^2z^2 = -38y^{5-2}z^{3-2} = -38y^3z
\]

3. **Rewrite the expression**:
After factoring out the GCF, we can rewrite the expression as:

\[
45x^2y^2z^2 - 38y^5z^3 = y^2z^2(45x^2 - 38y^3z)
\]

4. **Final factored form**:
Therefore, the fully factored expression is:

\[
\boxed{y^2z^2(45x^2 - 38y^3z)}
\]

This gives you the expression factored completely, with the common factor outside the parentheses.