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 }*5*5* a* a* a* a* a* b* b \\ 6a^3b^4\text{ = 2}*3* a* a* a* b* b* b* b \\ 12a^4b^4\text{ = 2 }*2*3* a* a* a* a* b* b* b* b \end{gathered}`

From the above factorisation

The Greatest common factor is

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

Therefore the greatest common factor is

`2a^3b^2`