Common Factor

A common factor of two or more numbers is a number that divides each of the given numbers without leaving a remainder.

Finding Common Factors

To find the common factors of two or more numbers, you can list all the factors of each number and then identify the factors that are common to all the numbers.

Example:

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 of 12 and 18: 1, 2, 3, 6

Greatest Common Factor (GCF)

The greatest common factor (GCF) of two or more numbers is the largest number that is a factor of each of the given numbers.

Finding the GCF

To find the GCF of two or more numbers, you can list all the factors of each number and then identify the greatest common factor among them.

Example:

Find the GCF of 24 and 36.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common factors of 24 and 36: 1, 2, 3, 4, 6, 12

Greatest common factor (GCF) of 24 and 36: 12

Study Guide

To master the concept of common factors and greatest common factor (GCF), follow these steps:

Understand the definition of a common factor and how to find common factors of given numbers.
Practice listing the factors of different numbers to identify common factors.
Learn how to identify the greatest common factor (GCF) among the common factors of given numbers.
Practice finding the GCF of different pairs of numbers to reinforce the concept.
Challenge yourself with word problems and real-life scenarios that involve finding common factors and GCF.

By understanding common factors and GCF, you'll be better equipped to work with multiples, fractions, and simplifying expressions in math.

◂Math Worksheets and Study Guides Sixth Grade. Ratio

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Grade 6 Curriculum Focal Points (NCTM)

Number and Operations: Connecting ratio and rate to multiplication and division

Students use simple reasoning about multiplication and division to solve ratio and rate problems (e.g., 'If 5 items cost $3.75 and all items are the same price, then I can find the cost of 12 items by first dividing $3.75 by 5 to find out how much one item costs and then multiplying the cost of a single item by 12'). By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of quantities, students extend whole number multiplication and division to ratios and rates. Thus, they expand the repertoire of problems that they can solve by using multiplication and division, and they build on their understanding of fractions to understand ratios. Students solve a wide variety of problems involving ratios and rates.