Understanding GCF and LCM through Prime Factorization

The video tutorial explains how to determine the greatest common factor (GCF) and least common multiple (LCM) of the numbers 36 and 60 using prime factorization and a Venn diagram. It begins by finding the prime factors of each number, then uses a Venn diagram to identify common factors for the GCF and all factors for the LCM. The GCF is calculated as 12, and the LCM is determined to be 180. The tutorial emphasizes the importance of understanding prime factorization and the use of Venn diagrams in solving these types of problems.

What are the two mathematical concepts being explored in this tutorial?

• Square Roots and Exponents

• Multiplication and Division

• Greatest Common Factor and Least Common Multiple

• Addition and Subtraction

What is the prime factorization of 36?

• 2 x 2 x 2 x 3

• 2^2 x 3^2

• 2 x 3 x 6

• 3 x 3 x 4

Which of the following is the prime factorization of 60?

• 3 x 5 x 4

• 2^2 x 3 x 5

• 2 x 2 x 2 x 5

• 2 x 3 x 10

In a Venn diagram, what does the intersection represent when finding the GCF?

• The sum of all prime factors

• All prime factors of both numbers

• Prime factors unique to each number

• Common prime factors of the numbers

What is the greatest common factor (GCF) of 36 and 60?

• 6

• 12

• 24

• 18

What is missing from the Venn diagram to complete the prime factors of 36?

• A factor of 2

• A factor of 3

• A factor of 5

• A factor of 6

Which prime factor is added to complete the prime factors of 60 in the Venn diagram?

• 6

• 5

• 3

• 2

What is the least common multiple (LCM) of 36 and 60?

• 120

• 150

• 210

• 180

How is the LCM determined using the Venn diagram?

• By dividing the GCF by the LCM

• By subtracting common factors

• By multiplying all prime factors in the union

• By adding all prime factors

Why is 180 considered the LCM of 36 and 60?

• It is the largest number divisible by both

• It is the smallest number that is a multiple of both

• It is the sum of all prime factors

• It is the difference between the two numbers