Finding Greatest Common Factors of Monomials

In this video, Anil Kumar explains how to find the greatest common factor (GCF) of monomials. The process involves using prime factorization to break down each monomial into its basic factors. By identifying the common factors between two monomials, the GCF can be calculated. The video provides examples with detailed steps to ensure understanding, concluding with a practice problem for viewers to solve.

What is the first step in finding the greatest common factor of monomials?

• Multiply the monomials together.

• Divide the monomials by their coefficients.

• Add the coefficients of the monomials.

• List all the factors of each monomial.

How can the number 12 be expressed using prime factorization?

• 1 x 12

• 2 x 2 x 3

• 3 x 4

• 2 x 6

What are the prime factors of 18?

• 2 x 9

• 2 x 3 x 3

• 3 x 3 x 2

• 1 x 18

Which of the following is a common factor of 12x^2y^3 and 18x^2y^2?

• 5

• 2

• y^3

• x^3

What is the greatest common factor of 12x^2y^3 and 18x^2y^2?

• 6x^2y^2

• 12x^2y^3

• 18x^2y^2

• 3x^2y

What should you do after listing all the prime factors of the monomials?

• Add them together.

• Divide them by the largest factor.

• Identify the common factors.

• Subtract them.

In the second example, what is the common factor among the coefficients of 15 and 9?

• 15

• 9

• 3

• 5

Which variable is common in both monomials 15x^2y^3z and 9x^3yz^2?

• x^2

• y^3

• x^3

• z

What is the greatest common factor of the monomials 15x^2y^3z and 9x^3yz^2?

• 9x^3yz^2

• 15x^2y^3z

• 3x^2yz

• x^2y^3z

What is the purpose of finding the greatest common factor in monomials?

• To simplify the monomials.

• To find the sum of the monomials.

• To multiply the monomials.

• To divide the monomials.