Finding the Greatest Common Factor

This video tutorial explains how to find the greatest common factor (GCF) when variables are involved. It begins with a simple example of finding the GCF of x²y and xy, demonstrating the process of identifying common factors. The tutorial then progresses to more complex examples, such as finding the GCF of x³y²z and x²y³z², and finally, xy z⁴ and x²y⁴z². Each example is broken down step-by-step, showing how to identify the highest power of each variable that is common to both terms. The video encourages viewers to pause and try solving the problems independently before reviewing the solutions.

What is the main focus of this video tutorial?

• Finding the greatest common factor with numbers

• Understanding prime numbers

• Finding the greatest common factor with variables

• Solving quadratic equations

Why is it important to find the greatest common factor in algebra?

• To simplify expressions

• To solve linear equations

• To factor quadratic equations

• To find the least common multiple

What is the greatest common factor of x^2y and xy?

• x

• x^2

• y

• xy

In the example with x^2y and xy, what is the factorization of x^2y?

• x^2 * y^2

• x * x * y

• x^2 * y

• x * y

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

• Identify the smallest power of each variable

• Divide the variables

• Multiply the variables

• Add the exponents

What is the greatest common factor of x^2y^3 and xy^2?

• xy

• x^2y^2

• xy^2

• x^2y^3

What is the greatest common factor of x^5y^4 and x^3y^2?

• x^3y^2

• x^3y^4

• x^5y^4

• x^2y^2

What is the greatest common factor of x^3y^2z and x^2y^3z^2?

• x^3y^2z

• x^2y^3z^2

• x^2y^2z

• x^3y^3z^2

Which variable has the greatest common factor of y^2 in the complex example?

• None

• z

• y

• x

In the complex example, what is the greatest common factor for the z terms?

• z^2

• z^3

• z

• z^4