Question

Find the greatest common factor of the following monomials50a^5b^2 6a^3b^4 12a^4b^4

Answer 1

From the question;

We are to find the greatest common factor of the following monomials

$\begin{gathered} 50a^5b^2 \\ 6a^{3^{}}b^4 \\ 12a^4b^4 \end{gathered}$

solution

By prime factorisation

$\begin{gathered} 50a^5b^2\text{ = 2 }\times5\times5\times a\times a\times a\times a\times a\times b\times b \\ 6a^3b^4\text{ = 2}\times3\times a\times a\times a\times b\times b\times b\times b \\ 12a^4b^4\text{ = 2 }\times2\times3\times a\times a\times a\times a\times b\times b\times b\times b \end{gathered}$

From the above factorisation

The Greatest common factor is

$\begin{gathered} G\mathrm{}C\mathrm{}F\text{ = 2}\times a\times a\times a\times b\times b \\ G\mathrm{}C\mathrm{}F=2a^3b^2 \end{gathered}$

Therefore the greatest common factor is

$2a^3b^2$