# How do you find the greatest common factor of 36xy^3, 24y^2?

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Tony B Share
Dec 11, 2016

$12 {y}^{2}$

#### Explanation:

Write greatest common factor as GCF

$\textcolor{b l u e}{\text{Consider the variables "x" and } y}$

$x$ is only in one of them so it is not 'common'. Thus it is not included in the GCF

${y}^{2} \times y = {y}^{3}$ so $\textcolor{g r e e n}{{y}^{2} \text{ is part of the GCF}}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider the coefficients 36 and 24}}$

Using prime factors: If you have any doubts at all sketch a factor tree.

From this observe that the 'common' prime factors are

$\textcolor{g r e e n}{2 \times 2 \times 3 = 12 \text{ is part of the GCF}}$
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$\textcolor{b l u e}{\text{Putting it all together}}$

GCF $\to 12 {y}^{2}$

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