GCF of each pair of polynomials 27 y3z and 45 x2y

9y

To find the greatest common factor (GCF) of each pair of polynomials, we can factor each polynomial and identify the common factors.

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.

To find the greatest common factor (GCF) of two polynomials, you need to identify the common factors and determine the highest exponent for each shared factor.

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.

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.