Finding Common Factors and Prime Factorization

In this video, Anil Kumar explains how to find the greatest common factor (GCF) of monomials. The tutorial covers two examples, demonstrating the step-by-step process of identifying common factors and calculating the GCF. The video concludes with practice problems and solutions to reinforce the learning.

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

• Divide the monomials by their coefficients.

• Add the coefficients of the monomials.

• List all the factors of each monomial.

• Multiply the monomials together.

How can the number 12 be expressed using prime factorization?

• 2 x 2 x 3

• 3 x 4

• 1 x 12

• 2 x 6

In the context of monomials, what does the term 'coefficient' refer to?

• The exponent of the variable.

• The constant term in the monomial.

• The variable part of the monomial.

• The sum of all factors.

What are the prime factors of 18?

• 2 x 9

• 3 x 6

• 2 x 3 x 3

• 1 x 18

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 the monomials 12x²y³ and 18x²y²?

• 6x²y²

• 12x²y³

• 18x²y²

• 3x²y²

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

• To divide the monomials.

• To simplify the monomials.

• To identify the common factors.

• To multiply the monomials.

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

• 3x²yz

• 15x²y³z

• 9x³yz²

• x²y²z

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

• z

• y³

• x²

• x³

What is the common factor of the coefficients 15 and 9?

• 9

• 3

• 15

• 5