Question

Factor the common factor out of each expression (GCF).-32m^5n - 36m^6n - 24m^5n^2________________________

Answer 1

In order to find the greatest common factor (GCF) of the terms, first let's factor the numeric values in their prime factors:

`\begin{gathered} 32=2\cdot2\cdot2\cdot2\cdot2\\ \\ 36=2\cdot2\cdot3\cdot3\\ \\ 24=2\cdot2\cdot2\cdot3 \end{gathered}`

The common factor between these three numbers is the product of the common prime factors, that is, 2 * 2 = 4.

Now, to find the common factor of the variables, we choose for each variable the one with the smaller exponent:

`\begin{gathered} m^5,m^6,m^5\rightarrow m^5\\ \\ n,n,n^2\rightarrow n\\ \\ \\ GCF=m^5n \end{gathered}`

Therefore the common factor is -4(m^5)n.

(we can put the negative signal as well, since all terms are negative).