Question

Find the greatest common factor of each set of monomials.

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

Short answer

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

Step-by-step solution

Step 1. Find the factorization of 21xy,28x2y and 42xy2.

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 21xy,28x2y and 42xy2. 

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 $7xy$.