Prime Factorization and GCF Concepts

Professor Dave explains the concept of greatest common factors (GCF), contrasting it with least common multiples. He provides examples using small numbers and demonstrates how to find the GCF by listing factors. For larger numbers, he introduces the prime factorization method, showing how to identify common prime factors and multiply them to find the GCF. The video concludes with an advanced example and a summary of the technique's reliability.

What is the greatest common factor of 10 and 15?

• 5

• 2

• 1

• 10

Which number is the greatest common factor of 18 and 24?

• 9

• 6

• 3

• 12

What is the first step in finding the greatest common factor using prime factorization?

• Find the prime factors of each number

• Add the numbers

• Multiply the numbers

• List all factors of the numbers

In the prime factorization method, what do you do after identifying common prime factors?

• Subtract them

• Divide them

• Multiply them together

• Add them together

What is the greatest common factor of 24 and 108 using prime factorization?

• 8

• 18

• 12

• 6

Why is prime factorization a better strategy for larger numbers?

• It is more accurate

• It is faster

• It is easier to understand

• It avoids listing all factors

What is the prime factorization of 24?

• 2 x 2 x 3 x 3

• 3 x 3 x 2

• 2 x 3 x 4

• 2 x 2 x 2 x 3

What is the prime factorization of 108?

• 2 x 3 x 3 x 3

• 2 x 2 x 3 x 3 x 3

• 3 x 3 x 3 x 3

• 2 x 2 x 2 x 3

Which of the following is NOT a step in finding the greatest common factor using prime factorization?

• List all factors

• Identify common prime factors

• Multiply common factors

• Perform prime factorization

What is the benefit of using prime factorization for finding the greatest common factor?

• It requires no calculations

• It is a traditional method

• It is less time-consuming for large numbers

• It is more fun