Greatest Common Factor and Prime Factorization

Professor Dave explains the concept of greatest common factors (GCF) by comparing it to least common multiples. He demonstrates how to find the GCF of two numbers by listing their factors and identifying the largest common factor. For larger numbers, he introduces the prime factorization method, which involves breaking down numbers into their prime factors and multiplying the common factors. This method is shown to be more efficient for larger numbers. The video concludes with a call to action for viewers to subscribe and support the channel.

What is the greatest common factor of two numbers?

• The smallest number that is a multiple of both numbers

• The difference between the two numbers

• The largest number that is a factor of both numbers

• The sum of the two numbers

Which of the following is the greatest common factor of 10 and 15?

• 5

• 10

• 3

• 2

What is the greatest common factor of 18 and 24?

• 9

• 6

• 12

• 3

Why is it easier to find the greatest common factor for smaller numbers?

• They have fewer factors to list and compare

• They are always prime numbers

• They have more factors to choose from

• They are closer to zero

What is a challenge when finding the greatest common factor for larger numbers?

• They are always even numbers

• They are always odd numbers

• They have too many factors to list easily

• They have no factors

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

• Add the numbers together

• List all factors of the numbers

• Break down each number into its prime factors

• Multiply the numbers together

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

• Subtract the prime factors from each other

• Identify common prime factors and multiply them

• Add all the prime factors together

• Multiply all the prime factors together

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

• 12

• 10

• 8

• 6

Why is the prime factorization method preferred for larger numbers?

• It is faster and more reliable

• It is the only method available

• It only works for even numbers

• It requires no calculations

What is the prime factorization of 24?

• 2 x 2 x 2 x 3

• 2 x 3 x 3

• 3 x 3 x 3

• 2 x 2 x 3 x 3