Q. 340 - Intermediate Algebra

Question

In the following exercises, find the greatest common factor.  

$45x^3{y}^2,15x^{4}y,10x^5{y}^3$

Step-by-Step Solution

Answer

The greatest common factor is $5x^{3}y$.

Step 1. Given information.

The expressions are,

$45x^3{y}^2,15x^{4}y,10x^5{y}^3$.

Step 2. Finding the greatest common factor.

Now, the factored form of the given expressions is 

$$\begin{gathered} 45x^3{y}^2=3\times 3\times 5\times x\times x\times x\times y\times y \\ 15x^{4}y=3\times 5\times x\times x\times x\times x\times y \\ 10x^5{y}^3=2\times 5\times x\times x\times x\times x\times x\times y\times y\times y \end{gathered}$$

Then the common facts are

$5\times x\times x\times x\times y=5x^{3}y$

Hence, the greatest common factor is $5x^{3}y$.