Question

Find the common factors of: $16x^3,-4x^2,32x$

Answer 1

Determine the common factors

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

Given,

$16x^3,-4x^2,32x$

The factors of the numbers $16x^3,-4x^2,32x$ are

$$\begin{gathered} 16x^3=2\times 2\times \mathbf{2}\mathbf{\times }\mathbf{2}\mathbf{\times }\mathit{x}\times x\times x \\ -4x^2=-1\times \mathbf{2}\mathbf{\times }\mathbf{2}\mathbf{\times }\mathit{x}\times x \\ 32x=2\times 2\times 2\times \mathbf{2}\mathbf{\times }\mathbf{2}\mathbf{\times }\mathit{x} \end{gathered}$$

On observing these factors, we can conclude that

Common factor $\begin{array}{rcl}& =& 2\times 2\times x\end{array}$

$\begin{array}{rcl}& =& 4x\end{array}$

Hence, the common factor of $16x^3,-4x^2,32x$ is $4x$.