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

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

In this Grade 4 Eureka Math lesson, students learn to use division to test whether a number is a factor of a larger number by checking for a remainder, and apply the associative property to identify additional factors. Students practice finding factor pairs, distinguishing prime from composite numbers, and recognizing divisibility patterns with multi-digit numbers. This lesson is part of Chapter 14: Reasoning with Divisibility and builds foundational skills for understanding number relationships.

Section 1

Identifying Factors with Division

Property

A number, bb, is a factor of another number, aa, if the division of aa by bb results in a remainder of 00.

Examples

Section 2

Finding New Factors with the Associative Property

Property

If a number is expressed as a product of factors, you can multiply those factors together in groups to find new factors. If N=a×b×cN = a \times b \times c, then the product (a×b)(a \times b) is also a factor of NN.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Identifying Factors with Division

Property

A number, bb, is a factor of another number, aa, if the division of aa by bb results in a remainder of 00.

Examples

Section 2

Finding New Factors with the Associative Property

Property

If a number is expressed as a product of factors, you can multiply those factors together in groups to find new factors. If N=a×b×cN = a \times b \times c, then the product (a×b)(a \times b) is also a factor of NN.

Examples