Understanding the Greatest Common Factor

This video tutorial explains how to determine the greatest common factor (GCF) of numbers using prime factorization. It covers the definition of GCF, provides examples with integers and variables, and demonstrates the process with trinomials. The video concludes with a brief mention of the least common multiple (LCM) as a related concept.

What is the greatest common factor (GCF) of two or more non-zero integers?

• The sum of the integers

• The smallest positive integer that divides the numbers without a remainder

• The largest positive integer that divides the numbers without a remainder

• The product of the integers

How is the greatest common denominator related to the greatest common factor?

• It is the sum of the greatest common factors

• It is the greatest common factor of the denominators

• It is unrelated to the greatest common factor

• It is the greatest common factor of the numerators

What is the GCF of 18 and 84 using prime factorization?

• 12

• 6

• 9

• 3

Which of the following is a step in determining the GCF of two numbers?

• Adding the numbers

• Finding the prime factorization of each number

• Dividing the larger number by the smaller

• Subtracting the smaller number from the larger

What is the GCF of 60 and 72?

• 18

• 12

• 10

• 6

When introducing variables, what remains the same in the procedure to find the GCF?

• The result of the GCF

• The order of operations

• The method of prime factorization

• The numbers used

What is the GCF of 27x^2y^2 and 15x^3y?

• 27xy

• 3x^2y

• 3xy

• 15x^2y

In the context of GCF, what does the least exponent on a variable indicate?

• The lowest power of the variable

• The power of the variable in the LCM

• The power of the variable in the GCF

• The highest power of the variable

What is the GCF of the trinomials x^2 - 4x + 3 and x^2 - x - 6?

• x + 1

• x - 3

• x + 3

• x - 1

What is a common confusion when learning about GCF?

• Confusing it with the average of the numbers

• Confusing it with the sum of the numbers

• Confusing it with the least common multiple

• Confusing it with the product of the numbers