Question

Find the common factors of: $3x^2{y}^3,10x^3{y}^2,6x^2{y}^{2}z$

Answer 1

Determine the common factor:

A factor of a number is a number that divides the given number evenly.

If a number is a factor of two or more numbers. then such a number is called a common factor.

Given numbers,

$3x^2{y}^3$, $10x^3{y}^2$ and $6x^2{y}^{2}z$.

The factors of the number $3x^2{y}^3$, $10x^3{y}^2$ and $6x^2{y}^{2}z$ are,

$$\begin{gathered} 3x^2{y}^3=1\times 3\times x\times x\times y\times y\times y \\ 10x^3{y}^2=1\times 2\times 5\times x\times x\times x\times y\times y \\ 6x^2{y}^{2}z=1\times 2\times 3\times x\times x\times y\times y\times z \end{gathered}$$

On observing these factors we can conclude that,

Common factor$\begin{array}{rcl}& =& 1\times x\times x\times y\times y\end{array}$

$\begin{array}{rcl}& =& x^2{y}^2\end{array}$

Hence, the common factor of $3x^2{y}^3$, $10x^3{y}^2$ and $6x^2{y}^{2}z$ is $x^2{y}^2$.