Factors of 27y^3z = 1,3,5,9,27,y,y^2.
Factors of 45x^2y = 1,3.5,9,15,45,x,y.
CF = 1,3,5,9,y.
GCF = 9.
Factors of 45x^2y = 1,3.5,9,15,45,x,y.
CF = 1,3,5,9,y.
GCF = 9.
The first polynomial, 27y^3z, can be factored as follows:
27y^3z = 3^3 * y^3 * z
The second polynomial, 45x^2y, can be factored as follows:
45x^2y = 3^2 * 5 * x^2 * y
Now let's compare the factors of these two polynomials to identify the common factors.
The common factors in 27y^3z and 45x^2y are:
3 (from the first polynomial)
y (from both polynomials)
Therefore, the GCF of 27y^3z and 45x^2y is 3y.
Let's find the GCF for the given pair of polynomials: 27y^3z and 45x^2y.
Step 1: Identify the factors of each polynomial.
Factors of 27y^3z: 1, 3, 9, 27, y, y^2, y^3, z, yz, y^2z, y^3z.
Factors of 45x^2y: 1, 3, 5, 9, 15, 45, x, x^2, y, xy, x^2y.
Step 2: Compare the factors and find common factors.
The common factors are 1, 3, 9, and y.
Step 3: Determine the highest exponent for each common factor.
9 is the highest exponent for the common factor 3 in 27y^3z (3^3 = 27), and 1 is the highest exponent for the common factor y in both polynomials.
Step 4: Combine the common factors with the highest exponent.
The GCF of 27y^3z and 45x^2y is 3y.
Therefore, the greatest common factor of the polynomials 27y^3z and 45x^2y is 3y.