Finding Greatest Common Factors and Prime Factorization

In this video, Anil Kumar explains how to find the greatest common factor (GCF) of monomials using prime factorization. The video covers two examples: 12x²y³ and 18x²y², and 15x²y³z and 9x³yz². The process involves breaking down each monomial into its prime factors, identifying common factors, and then calculating the GCF. The video concludes with a summary and encourages viewers to practice the method.

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

• Subtract the smaller monomial from the larger one.

• List all the factors of each monomial.

• Add the coefficients of the monomials.

• Multiply the monomials together.

How can the number 12 be expressed using prime factorization?

• 2 x 6

• 3 x 4

• 2 x 2 x 3

• 1 x 12

What are the prime factors of 18?

• 2 x 3 x 3

• 3 x 6

• 1 x 18

• 2 x 9

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

• x³

• z

• 2

• y³

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

• 6x²y²

• 12x²y³

• 18x²y²

• 3x²y

What is the greatest common factor of the numbers 15 and 9?

• 9

• 15

• 5

• 3

Which variable is common in the monomials 15x²y³z and 9x³yz²?

• y

• z²

• x²

• x³

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

• 9x³yz²

• 3x²yz

• x²y

• 15x²y³z

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

• To find common factors.

• To identify the largest number.

• To divide the monomials.

• To simplify the monomials.

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

• Add them together.

• Identify the common factors.

• Multiply them by 2.

• Subtract the smaller from the larger.