Question

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

Answer 1

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 `5xy`

Explanation:

`10xy^2=2*5*x*y*y`

`5x^2y=5*x*y*y`

`20x^3y=2*2*5*x*y*y*y`

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

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