Q16. - Algebra 1

Question

Find the greatest common factor of each set of monomials.

$21xy,28x^{2}y,42x{y}^2$

Step-by-Step Solution

Answer

The greatest common factor of the given set of monomials is $\mathbf{7}\mathit{x}\mathit{y}$.

Step 1. Find the factorization of 21 x y , 28 x 2 y and 42 x y 2 .

Find the factorization of $21xy$,$28x^{2}y$ and $42x{y}^2$.

$$\begin{gathered} 21xy=3\cdot 7\cdot x\cdot y \\ 28x^{2}y=2\cdot 2\cdot 7\cdot x\cdot x\cdot y \\ 42x{y}^2=2\cdot 3\cdot 7\cdot x\cdot y\cdot y \end{gathered}$$

Step 2. Find the greatest common factor of 21 x y , 28 x 2 y and 42 x y 2 .

From the factorization of $21xy,28x^{2}y$ and $42x{y}^2$, it can be noticed that the greatest common factor of $21xy,28x^{2}y$ and $42x{y}^2$ is $7\cdot x\cdot y$ or $7xy$.

Therefore, the greatest common factor of the given set of monomials is $7xy$.