How do you find the gcf of 10xy^2 + 5x^2y - 20x^3y?

Jun 23, 2015

You can factor each individual term then identify which factors occur in all terms and with what multiplicity. Then multiply those common factors together.

In your example the gcf is $5 x y$

Explanation:

$10 x {y}^{2} = 2 \cdot 5 \cdot x \cdot y \cdot y$

$5 {x}^{2} y = 5 \cdot x \cdot y \cdot y$

$20 {x}^{3} y = 2 \cdot 2 \cdot 5 \cdot x \cdot y \cdot y \cdot y$

For all of the three terms, the factors $5$, $x$ and $y$ occur once. So just multiply them together to get the gcf $5 x y$.

If the first term were $10 {x}^{2} {y}^{2}$ then $x$ would be a factor of all terms with a multiplicity of 2 and the gcf would be $5 {x}^{2} y$