Prime Factorization Concepts and Problems

The video tutorial from MooMooMath explains prime factorization, a method to find the smallest prime numbers that multiply to a given number. Using the example of 72, the instructor demonstrates the process of drawing branches from composite numbers until reaching prime numbers. The tutorial covers the rules of prime factorization, such as not drawing branches from prime numbers and listing factors from smallest to largest. The example is worked through twice to show different methods, resulting in the prime factorization of 72 as 2 cubed times 3 squared.

What is the main goal of prime factorization?

• To find the largest prime numbers that add up to a given number.

• To identify the smallest prime numbers that multiply to form a given number.

• To divide a number into even parts.

• To convert a number into a decimal.

Which of the following is a composite number?

• 2

• 5

• 4

• 3

What should you do when you encounter a prime number during factorization?

• Ignore it and move on.

• Convert it to a composite number.

• Continue drawing branches.

• Stop drawing branches.

In the example of 72, what are the two numbers that 72 is initially divided into?

• 7 and 10

• 5 and 14

• 8 and 9

• 6 and 12

How does the number 8 factor further in the example?

• 4 times 2

• 5 times 1

• 3 times 3

• 2 times 4

What is the prime factorization of 72?

• 2^3 * 3^3

• 2^2 * 3^3

• 2^3 * 3^2

• 3^3 * 2^2

How many times does the number 2 appear in the prime factorization of 72?

• Twice

• Four times

• Once

• Three times

What is the exponent of 3 in the prime factorization of 72?

• 3

• 1

• 4

• 2