Question

identify the greatest common factor of $9c^{3}z^{2}$ and $9c^{4}z^{3}$.

Explanation:

Step1: Analyze coefficient

The coefficients of both terms are 9, so the common - coefficient factor is 9.

Step2: Analyze variable c

For the variable c, in $9c^{3}z^{2}$ the power of c is 3 and in $9c^{4}z^{3}$ the power of c is 4. The lowest power of c between them is $c^{3}$.

Step3: Analyze variable z

For the variable z, in $9c^{3}z^{2}$ the power of z is 2 and in $9c^{4}z^{3}$ the power of z is 3. The lowest power of z between them is $z^{2}$.

Step4: Combine factors

The greatest common factor is the product of the common - coefficient factor and the common - variable factors, which is $9c^{3}z^{2}$.

Answer:

$9c^{3}z^{2}$