Lesson 4.1

Prime Factorization

Essential Question: How do you write a number as a product of primes?

Before we start…

Members of the art club are learning to do calligraphy. Their first project is to make posters to display their new lettering style. A poster will display 36 characters in order: the 26 uppercase letters of the alphabet and the digits 0 through 9.

The art club members want the characters arranged in a rectangular display with the same number of characters in each row. What are some possibilities?

What is a factor?

• A factor is any whole number that can be divided exactly into another number.

• 1, 2, 3, and 6 are factors of 6.

Write all the factors of the number.

Field Trip A class of 36 students is on a field trip at the aquarium. The teacher wants to break the class into groups of the same size. Find all the possible group sizes.

Photos A photographer wants to arrange 40 students in rows of the same length. What are the possible row lengths the photographer can arrange the students in?

What is a prime number?

• A prime number is a whole number greater than 1 whose only positive factors are 1 and itself.

• 2, 3, 5, 7, 11, 13, 17 are all examples of prime numbers.

What is a composite number?

• A composite number is a whole number greater than 1 that has positive factors other than 1 and itself.

• 4, 12, 20, 36 are all examples of composite numbers.

What about 1?

• 1 is neither a prime nor a composite number.

Write all the factors and tell if it’s prime or composite.

Write all the factors and tell if it’s prime or composite.

Write all the factors and tell if it’s prime or composite.

Write all the factors and tell if it’s prime or composite.

Is the statement true or false?

The prime factors of 15 are 1, 3, and 5.

All even numbers are composite.

Is the statement true or false?

The product of any two numbers is composite.

The product of any two prime numbers is always odd.

What is prime factorization?

• Prime factorization is when you write a whole number as the product of prime numbers.

• One way to find the prime factorization of a number is to use a factor tree.

What is a factor tree?

• A factor tree is a diagram showing all the prime factors of a number.

How do you write a number as a product of primes?

• You will use a factor tree to help you. • Once factored, you will write the number as a

product of its prime factors.

Write the prime factorization of 54

Write the prime factorization of 24

Write the prime factorization of 73

Write the prime factorization of 30

Write the prime factorization of 40

Write the prime factorization of 55

Write the prime factorization of 48

• How do you write a number as a product of primes?

Ticket Out the Door

Write the prime factorization of 75