Chapter 6, Problem 1RE

For Exercises 1-4, identify the greatest common factor for each group of terms.

$15a^2{b}^4,30a^{3}b,9a^5{b}^3$

To determine

The greatest common factors from the provided group of expressions $15a^2{b}^4,30a^{3}b,\text{and }9a^5{b}^3$.

Answer to Problem 1RE

Solution:

The greatest common factor of the provided group of expressions $15a^2{b}^4,30a^{3}b,\text{and }9a^5{b}^3$ is $3a^{2}b$.

Explanation of Solution

Given information:

The provided expressions is

$15a^2{b}^4,30a^{3}b,\text{and }9a^5{b}^3$

Expression:

Consider the provided expressions:

$15a^2{b}^4,30a^{3}b,\text{and }9a^5{b}^3$

List all factor of the provided expressions:

$\begin{array}{c}15a^2{b}^4=\begin{array}{c}3\end{array}\cdot 5\cdot a^2\cdot b^4\\ 30a^{3}b=2\cdot 3\cdot 5\cdot a^3\cdot b\\ 9a^5{b}^3=3^2\cdot a^5\cdot b^3\end{array}$,

The common factors in provided three expressions are $3,a$, and $b$.

The lowest power of 3 is 1.

The lowest power of a is 2.

The lowest power of b is 1.

From above explanation, the greatest common factor of the provided expression can be written as

$\text{GCF}=3a^{2}b$

Therefore, the greatest common factor of the provided expressions $15a^2{b}^4,30a^{3}b,\text{and }9a^5{b}^3$ is $3a^{2}b$.