Find the GCF (greatest common factor ) of the following terms.
{5xy^2,25x^2,15x^2 y^2}
To find the GCF (greatest common factor) of these terms, we need to look for the highest power of each variable that appears in all three terms.
Let's break down the variables and their powers in each term:
1) 5xy^2:
- The highest power of x is 1.
- The highest power of y is 2.
2) 25x^2:
- The highest power of x is 2.
- There is no y term.
3) 15x^2y^2:
- The highest power of x is 2.
- The highest power of y is 2.
Now, let's determine the common factors for each variable:
- For x, the common factor is x^2 (the highest power that appears in all three terms).
- For y, the common factor is y^2 (the highest power that appears in all three terms).
Therefore, the GCF of the given terms is x^2y^2.