Common Factor Study Guide

Let's explore the concept of common factors and how they are used in mathematics.

What is a Common Factor?

A common factor of two or more numbers is a number that divides each of the given numbers evenly. In other words, it is a number that is a factor of all the given numbers.

Finding Common Factors

To find the common factors of a set of numbers, you can start by listing the factors of each number. Then, identify the factors that are common to all the numbers in the set.

Example

Let's find the common factors of 12 and 18:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6

Using Common Factors

Common factors are often used in simplifying fractions and finding the greatest common factor (GCF) of a set of numbers. They are also useful in determining the common denominators when adding or subtracting fractions.

Practice Exercise

Find the common factors of 24 and 36:

List the factors of 24
List the factors of 36
Identify the common factors

Conclusion

Understanding common factors is important in various mathematical operations, especially in working with fractions and simplifying expressions. Practice identifying common factors to strengthen your skills in this area.

◂Math Worksheets and Study Guides Fifth Grade. Division

Study Guide

Division

Activity Lesson

Matching Division Cards

Vocabulary/Answer key

Division

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Grade 5 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers

Students apply their understanding of models for division, place value, properties, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select appropriate methods and apply them accurately to estimate quotients or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for dividing whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems. They consider the context in which a problem is situated to select the most useful form of the quotient for the solution, and they interpret it appropriately.

Connections to the Grade 5 Focal Points (NCTM)

Number and Operations: Building on their work in grade 4, students extend their understanding of place value to numbers through millions and millionths in various contexts. They apply what they know about multiplication of whole numbers to larger numbers. Students also explore contexts that they can describe with negative numbers (e.g., situations of owing money or measuring elevations above and below sea level).

Common Factor Study Guide

What is a Common Factor?

Finding Common Factors

Example

Using Common Factors

Practice Exercise

Conclusion

[Common Factor] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Fifth Grade. Division

The resources above cover the following skills: