Learn on PengiEureka Math, Grade 4Chapter 14: Reasoning with Divisibility

Lesson 4: Explore properties of prime and composite numbers to 100 by using multiples.

In this Grade 4 Eureka Math lesson from Chapter 14, students explore the properties of prime and composite numbers up to 100 by using the Sieve of Eratosthenes to systematically cross out multiples and identify which numbers remain. Students practice distinguishing between factors and multiples, recognize that multiples are infinite while factors are finite, and determine whether numbers are prime or composite based on their factor pairs. By the end of the lesson, students can identify all prime and composite numbers to 100 and explain why certain numbers, like 1, fit neither category.

Section 1

Identifying Even Composite Numbers

Property

All even numbers greater than 2 are composite numbers. This is because they are divisible by 2, meaning they have 2 as a factor in addition to 1 and the number itself.

Examples

Section 2

Finding Prime Numbers Using the Sieve of Eratosthenes

Property

The Sieve of Eratosthenes is an algorithm for finding all prime numbers up to a specified limit. It works by creating a list of integers and systematically eliminating composite numbers by crossing out the multiples of each prime, starting with the first prime number, 2. The numbers that are not crossed out are the prime numbers.

Examples

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Chapter 14: Reasoning with Divisibility

  1. Lesson 1

    Lesson 1: Find factor pairs for numbers to 100, and use understanding of factors to define prime and composite.

  2. Lesson 2

    Lesson 2: Use division and the associative property to test for factors and observe patterns.

  3. Lesson 3

    Lesson 3: Determine if a whole number is a multiple of another number.

  4. Lesson 4Current

    Lesson 4: Explore properties of prime and composite numbers to 100 by using multiples.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Identifying Even Composite Numbers

Property

All even numbers greater than 2 are composite numbers. This is because they are divisible by 2, meaning they have 2 as a factor in addition to 1 and the number itself.

Examples

Section 2

Finding Prime Numbers Using the Sieve of Eratosthenes

Property

The Sieve of Eratosthenes is an algorithm for finding all prime numbers up to a specified limit. It works by creating a list of integers and systematically eliminating composite numbers by crossing out the multiples of each prime, starting with the first prime number, 2. The numbers that are not crossed out are the prime numbers.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 14: Reasoning with Divisibility

  1. Lesson 1

    Lesson 1: Find factor pairs for numbers to 100, and use understanding of factors to define prime and composite.

  2. Lesson 2

    Lesson 2: Use division and the associative property to test for factors and observe patterns.

  3. Lesson 3

    Lesson 3: Determine if a whole number is a multiple of another number.

  4. Lesson 4Current

    Lesson 4: Explore properties of prime and composite numbers to 100 by using multiples.