Chapter CSB1.2, Problem 27E

To determine

Tofind:The GCF on given monomials.

Answer to Problem 27E

The GCF of $21x^{2}y$ and $63x{y}^2$ is $21xy$ .

Explanation of Solution

Given information:

The given monomials are $21x^{2}y$ and $63x{y}^2$ .

Formulaused:

The greatest number or expression which is a factor of two (or more) other numbers or polynomials is called the Greatest Common Factors (GCF). To find the GCF we find all the factors of two or more polynomials, and choose factors that are the common, and then the product of common factors is the Greatest Common Factor.

Calculations:

The given monomials are $21x^{2}y$ and $63x{y}^2$ .

The factors of given monomials are

  $21x^{2}y=3\times 7\times x\times x\times y$

  $63x{y}^2=3\times 3\times 7\times x\times y\times y$

The common factors of $21x^{2}y$ and $63x{y}^2$ are 3, 7, x and y .

Hence, the GCF of $21x^{2}y$ and $63x{y}^2$ is $3\times 7\times x\times y=21xy$

Conclusion:

The GCF of $21x^{2}y$ and $63x{y}^2$ is $21xy$ .