Understanding Greatest Common Factor of Monomials

The video tutorial explains how to find the greatest common factor (GCF) of monomials. It begins by defining the GCF and its application in algebraic expressions. The tutorial then demonstrates the process of breaking down numbers and variables into their prime factors. Finally, it shows how to identify the common factors between two monomials to determine their GCF.

What is the greatest common factor (GCF) of two monomials?

• The difference between the factors of both monomials

• The sum of the factors of both monomials

• The smallest factor that divides both monomials

• The largest factor that divides both monomials

Why is it important to consider the 'greatest' in algebraic expressions?

• Because it includes the most factors of each monomial

• Because it eliminates negative values

• Because it simplifies the expression to a single number

• Because it always results in the largest number

What is the first step in finding the GCF of monomials?

• Breaking down each number into its prime factorization

• Multiplying the monomials together

• Subtracting the exponents of the variables

• Adding the coefficients of the monomials

How is the prime factorization of a number used in finding the GCF?

• It simplifies the monomial to a single term

• It helps in identifying the common factors

• It determines the sum of the factors

• It eliminates the need for variable consideration

In the example, what is the prime factorization of 10?

• 5 x 5

• 2 x 5

• 2 x 3

• 3 x 3

What is the GCF of the monomials 10cd² and 25c³d²?

• 5cd²

• 10c²d²

• 5cd

• 25c³d²

Which factor is common in both 10cd² and 25c³d²?

• d³

• c²

• 5

• 2

How many 'd' factors are common in both monomials?

• None

• Three

• Two

• One

Why might the GCF not be the greatest possible number?

• Because it is always a positive integer

• Because it ignores variable factors

• Because it only considers numeric factors

• Because variables can take negative or fractional values

What does the GCF ensure about the monomials?

• It is the sum of both monomials

• They have no common factors

• It is divisible into both monomials

• They are both prime numbers