Finding the Greatest Common Factor

The video tutorial explains how to find the greatest common factor (GCF) when dealing with exponents and variables. It begins with a demonstration of finding the GCF of 70 and 14 using a factor tree method, identifying prime numbers, and organizing them in a chart. The tutorial then extends the concept to include variables and exponents, showing how to determine the GCF of expressions like 70y^2x and 14x^2y, resulting in a GCF of 14YX.

What is the first step in finding the greatest common factor when dealing with exponents and variables?

• Divide the numbers by the smallest prime number.

• Add all the numbers together.

• Use a factor tree to break down numbers.

• Identify the least common multiple.

Which pair of numbers is used to start the factor tree for 70?

• 7 and 10

• 3 and 23

• 5 and 14

• 2 and 35

What are the prime factors of 35?

• 6 and 6

• 5 and 7

• 3 and 11

• 2 and 17

What are the prime factors of 14?

• 3 and 5

• 2 and 7

• 4 and 3

• 6 and 2

How do you organize the prime factors to find the GCF of 70 and 14?

• Divide the largest prime factor by the smallest.

• Multiply all the prime factors together.

• Create a chart and look for common columns.

• List them in ascending order.

What is the GCF of 70 and 14?

• 2

• 7

• 14

• 35

When finding the GCF of expressions with variables, what should you do if a variable is present in both expressions?

• Ignore the variable.

• Add the exponents of the variable.

• Include the variable in the GCF.

• Subtract the exponents of the variable.

What is the GCF of the expressions 70y^2x and 14x^2y?

• 70xy

• 14x^2y^2

• 14xy

• 7x^2y^2

Which of the following is NOT a step in finding the GCF of expressions with variables?

• Identify common variables.

• Use the smallest exponent for common variables.

• Multiply all coefficients together.

• Find the GCF of the coefficients.