Determining GCF and LCM with Prime Factors and Venn Diagrams

The video tutorial explains how to determine the greatest common factor (GCF) and least common multiple (LCM) of the numbers 12 and 16 using prime factorization and Venn diagrams. It begins with the prime factorization of both numbers, then uses a Venn diagram to identify common factors for the GCF. The tutorial continues by completing the Venn diagram to find the LCM, demonstrating that the LCM is the smallest number divisible by both 12 and 16. The video concludes with a recap of the process and the results.

What two mathematical concepts are being determined for the numbers 12 and 16?

• Square and Cube

• Product and Quotient

• Greatest Common Factor and Least Common Multiple

• Sum and Difference

What is the prime factorization of 12?

• 3 x 3 x 3

• 2 x 2 x 2

• 2 x 3 x 3

• 2 x 2 x 3

How can the prime factorization of 16 be expressed using exponents?

• 2^5

• 2^2

• 2^3

• 2^4

What does the overlapping region in the Venn diagram represent?

• Non-prime factors

• Prime factors of 16 only

• Prime factors common to both 12 and 16

• Prime factors of 12 only

What is the greatest common factor (GCF) of 12 and 16?

• 2

• 4

• 6

• 8

Which prime factor is missing from the set on the left in the Venn diagram?

• 2

• 3

• 5

• 4

How many additional factors of 2 are missing from the set on the right in the Venn diagram?

• 3

• 2

• 1

• 4

What is the least common multiple (LCM) of 12 and 16?

• 48

• 24

• 36

• 60

Which of the following is true about the least common multiple (LCM)?

• It is the difference between the two numbers.

• It is the largest number that divides both numbers.

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

• It is the sum of the two numbers.

Why is 48 divisible by both 12 and 16?

• Because it is a prime number.

• Because it contains all the prime factors of both 12 and 16.

• Because it is an even number.

• Because it is a multiple of 10.