Find the GCF (greatest common factor) of the following terms. {36xy, 18xy^2, 54
To find the greatest common factor (GCF) of the given terms, we need to find the largest number or variable that divides evenly into all of the terms.
First, let's factor each term:
36xy = 2^2 * 3^2 * x * y
18xy^2 = 2 * 3^2 * x * y^2
54 = 2 * 3^3
Now, let's find the common factors:
The common factors for the numbers are 2 and 3.
The common factor for x is x.
The common factor for y is y.
Taking the smallest exponent for each variable and multiplying the common factors, we get:
GCF = 2 * 3 * x * y = 6xy.
Therefore, the GCF (greatest common factor) of 36xy, 18xy^2, and 54 is 6xy.