Understanding Greatest Common Factor of Monomials

The video tutorial explains how to determine the greatest common factor (GCF) of two monomials. It begins by defining the GCF as the monomial with the largest coefficient that divides the coefficients of the given monomials and shares the greatest number of common variable factors. The tutorial then demonstrates the process of finding the GCF by first determining the prime factorization of the coefficients 88 and 24. It also examines the variable factors, specifically focusing on the common factors of R. Finally, the video combines these common factors to calculate the GCF, which is 8R^13.

What is the greatest common factor of two monomials?

• The sum of the coefficients of the monomials

• The smallest whole number that divides the coefficients

• The monomial with the smallest number of variable factors

• The monomial with the greatest whole number that divides the coefficients and the greatest number of common variable factors

What is the prime factorization of 88?

• 2 * 2 * 2 * 11

• 2 * 3 * 11

• 3 * 3 * 11

• 2 * 2 * 3 * 11

Which of the following is the prime factorization of 24?

• 2 * 2 * 2 * 3

• 3 * 3 * 3

• 2 * 3 * 3

• 2 * 2 * 3 * 3

How many factors of R are common in the two monomials?

• 18

• None

• 5

• 13

What is the prime factorization of 88 R^18?

• 2 * 2 * 2 * 11 * R^13

• 2 * 2 * 2 * 11 * R^5

• 2 * 2 * 2 * 11 * R^13 * R^5

• 2 * 2 * 2 * 11 * R^18

What is the prime factorization of 24 R^13?

• 2 * 3 * 3 * R^13

• 2 * 2 * 2 * 3 * R^13

• 2 * 2 * 3 * R^13

• 3 * 3 * 3 * R^13

How many factors of two are common in both monomials?

• Two

• Three

• None

• Four

What is the greatest common factor of the two monomials?

• 4 R^18

• 4 R^13

• 8 R^13

• 8 R^18

Which step is crucial in determining the GCF of monomials?

• Multiplying the coefficients

• Subtracting the coefficients

• Finding the prime factorization of the coefficients

• Adding the coefficients

What is the final result of the GCF calculation in the video?

• 8 R^13

• 8 R^18

• 4 R^13

• 4 R^18