Finding the Greatest Common Factor

In this video, Anil Kumar explains how to find the greatest common factor (GCF) of monomials using prime factorization. The video covers two examples, demonstrating the process of breaking down monomials into their prime factors, identifying common factors, and calculating the GCF. The tutorial concludes with a practice problem and encourages viewers to apply the method independently.

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

• Add the coefficients of the monomials.

• Multiply the monomials together.

• Subtract the smaller monomial from the larger one.

• List all the factors of each monomial.

How can the number 12 be expressed using prime factorization?

• 3 x 4

• 2 x 6

• 1 x 12

• 2 x 2 x 3

What are the prime factors of 18?

• 1 x 18

• 2 x 3 x 3

• 3 x 6

• 2 x 9

Which of the following is a common factor of the monomials 12x²y³ and 18x²y²?

• x³

• y³

• 2

• z

What is the greatest common factor of 12x²y³ and 18x²y²?

• 12x²y³

• 18x²y²

• 3x²y

• 6x²y²

In the second example, what is the common factor among the variables x² and x³?

• x²

• x

• x³

• x⁴

What is the greatest common factor of the monomials 15x²y³z and 9x³yz²?

• 9x³yz²

• 3x²yz

• 15x²y³z

• x²y²z

Which of the following is NOT a step in finding the GCF of monomials?

• Listing all prime factors

• Identifying common factors

• Adding the coefficients

• Multiplying the common factors

What is the common factor of y³ and y in the second example?

• y²

• y³

• 1

• y

What is the purpose of prime factorization in finding the GCF of monomials?

• To simplify the monomials

• To divide the monomials

• To identify the common factors

• To multiply the monomials