Volume, Factors, and Prime Factorization

The video tutorial covers the prime factorization of natural numbers, solving problems involving prime numbers, and calculating the greatest common factor (GCF). It also includes a practical problem of determining how many cube-shaped boxes can fit into a shipping container without leaving any empty space. The tutorial emphasizes understanding prime factorization, factors, and the application of GCF in problem-solving.

If a natural number n is expressed as the product of two distinct prime numbers, how many factors does n have?

• 2

• 4

• 6

• 8

Given pn = 150, where p is a prime number, which of the following must be true?

• p is a factor of 20

• p is a factor of 10 or 15

• p is a factor of 30

• p is a factor of 25

What is the prime factorization of 150?

• 2 x 3 x 5

• 2 x 3 x 5 x 5

• 2 x 5 x 5

• 3 x 5 x 5

If the greatest common factor of n and 540 is 36, which of the following could be the prime factorization of n?

• 2^2 x 3^3

• 2^4 x 3^2 x 7

• 2 x 3^2

• 2^4 x 3^5

What is the prime factorization of 540?

• 2^2 x 3^3 x 5

• 2^2 x 3^2 x 5

• 2 x 3^2 x 5

• 2^3 x 3^2 x 5

What is the greatest common factor of 8, 12, and 24?

• 3

• 2

• 6

• 4

If a shipping container measures 8 feet by 12 feet by 24 feet, what is the largest size of cube-shaped boxes that can fit perfectly inside?

• 2 feet

• 3 feet

• 4 feet

• 6 feet

How many cube-shaped boxes of side 4 feet can fit in a container measuring 8 feet by 12 feet by 24 feet?

• 12

• 36

• 18

• 24

If the dimensions of a box are determined by the greatest common factor of the container's dimensions, what is the side length of the box?

• 2 feet

• 5 feet

• 3 feet

• 4 feet

What is the total number of boxes that can fit in the container if each box has a side length of 4 feet?

• 12

• 18

• 24

• 36