Find the GCF (greatest common factor ) of the following terms.
{5xy^(2),25x^(2),15x^(2)y^(2)}
To find the greatest common factor (GCF) of these terms, we need to find the highest power of each variable that appears in all the terms.
Let's break down each term:
5xy^2 can be broken down as 5 * x * y^2, so it has a factor of x and y^2.
25x^2 can be broken down as 25 * x^2, so it has a factor of x^2.
15x^2y^2 can be broken down as 15 * x^2 * y^2, so it has a factor of x^2 and y^2.
Now, we look for the common factors that appear in all the terms:
- The factor x appears in all three terms.
- The factor x^2 appears in two of the terms.
- The factor y^2 appears in two of the terms.
The highest power of x that appears in all three terms is x^2, and the highest power of y that appears in all three terms is y^2.
Therefore, the GCF of 5xy^2, 25x^2, and 15x^2y^2 is x^2y^2.