Chapter 8.1, Problem 17PPS

To determine

The GCF of each set of monomials.

Answer to Problem 17PPS

  $2z$

Explanation of Solution

Given:

The given monomials are:

  $26z^2,32z,44z^4$

Calculation:

The GCF of the given monomials can be calculated as:

Write the prime factorization of each monomial:

  $\begin{array}{l}=26z^2\\ =\left(2\times 13\right)\left(z\times z\right)\\ =2\times 13\times z\times z\end{array}$

and,

  $\begin{array}{l}=32z\\ =\left(2\times 2\times 2\times 2\times 2\right)\left(z\right)\\ =2\times 2\times 2\times 2\times 2\times z\end{array}$

and,

  $\begin{array}{l}=44z^4\\ =\left(2\times 2\times 11\right)\left(z\times z\times z\times z\right)\\ =2\times 2\times 11\times z\times z\times z\times z\end{array}$

Now, identify the common factors in all the factored monomials:

  $=2,z$

Therefore, the GCF will be:

  $\begin{array}{l}=2\times z\\ =2z\end{array}$