identify the greatest common factor of 42yz and 48z.

Explanation:

Step1: Prime - factorize the coefficients

Prime - factorize 42 and 48. $42 = 2\times3\times7$ $48 = 2\times2\times2\times2\times3$

Step2: Find GCF of coefficients

The common factors of 42 and 48 are 2 and 3. So, GCF of 42 and 48 is $2\times3=6$.

Step3: Consider variables

For the variables, both terms have $z$. The first term has $y$ which the second term does not have. So the common variable factor is $z$.

Step4: Combine GCF of coefficients and variables

The GCF of $42yz$ and $48z$ is the product of the GCF of the coefficients and the common variable factor, which is $6z$.

Answer:

$6z$