Chapter 8.1, Problem 2CCYP

To determine

The GCF of each pair of monomials.

Answer to Problem 2CCYP

  $10q^{2}rt$

Explanation of Solution

Given:

The given monomials are:

  $30q^3{r}^{2}t,50q^{2}rt$

Calculation:

The GCF of the given monomials can be calculated as:

Write the prime factorization of each monomial:

  $\begin{array}{l}=30q^3{r}^{2}t\\ =\left(2\times 3\times 5\right)\left(q\times q\times q\right)\left(r\times r\right)\left(t\right)\\ =2\times 3\times 5\times q\times q\times q\times r\times r\times t\end{array}$

and,

  $\begin{array}{l}=50q^{2}rt\\ =\left(2\times 5\times 5\right)\left(q\times q\right)\left(r\right)\left(t\right)\\ =2\times 5\times 5\times q\times q\times r\times t\end{array}$

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

  $=2,5,q,q,r,t$

Therefore, the GCF will be:

  $\begin{array}{l}=2\times 5\times q\times q\times r\times t\\ =10q^{2}rt\end{array}$