Question

Find the greatest common factor of thefollowing monomials:41g3h43g2 h7Enter the correct answer.

Answer 1

$\text{Greatest common factor = g}^2h$Explanation:

$\begin{gathered} \text{Given expressions:} \\ 41g^3h\text{ }and\text{ }43g^2h^2 \\ \\ We\text{ n}eed\text{ to find factors common to both expressions} \end{gathered}$

First let's expand each expression:

$\begin{gathered} 41g^3h\text{ = 41 }\times\text{ g }\times g\times g\times h \\ 43g^2h^2\text{ = 43 }\times g\text{ }\times\text{ g}\times h\times h \end{gathered}$

Next, we will pick the letters and numbers common to both:

$\begin{gathered} \text{Common factors: } \\ \text{g }\times\text{ g }\times h \end{gathered}$

$\begin{gathered} g\times g\times h=g^2h \\ \\ \text{The greatest common factor = }g^2h \end{gathered}$