Find the GCF (greatest common factor) of the following terms.
{54xy, 27xy^2, 81}
To find the GCF of these terms, we need to find the highest power of each prime factor that appears in all three terms.
First, let's look at the prime factorization of each term:
54xy = 2 * 3^3 * x * y
27xy^2 = 3^3 * x * y^2
81 = 3^4
Now, let's identify the highest power of each prime factor that appears in all three terms:
The highest power of 2 that appears in all three terms is 2^0.
The highest power of 3 that appears in all three terms is 3^3.
The highest power of x that appears in all three terms is x^1.
The highest power of y that appears in all three terms is y^0.
Therefore, the GCF of 54xy, 27xy^2, and 81 is 3^3 * x^1 = 27x.