# Ch 5: NES Middle Grades Math: Number Theory

### About This Chapter

## NES Middle Grades Math - Number Theory - Chapter Summary

This chapter on number theory is designed to contribute to your existing comprehension of multiples, factors, prime and composite numbers as well as the processes involved in prime factorization. Review the chapter's video lessons before you go on to take the NES Middle Grades Math examination. When you explore this chapter, you could increase your ability to:

- Define and differentiate between prime, composite, odd and even numbers
- Calculate a number's prime factorization
- Factor numbers with prime numbers and exponents
- Solve word problems with the greatest common factor and the least common multiple
- Find the least common multiple with prime factorization

Each of these short video lessons is narrated by a knowledgeable instructor. Prepare for the NES Middle Grades Math examination by watching or listening to the videos, referring to the accompanying transcripts and worksheets, and asking questions of the experts as necessary. When you feel you've got a firmer understanding of number theory, take the lesson quizzes. You can take them again if needed, then print out the results for future reference.

### NES Middle Grades Math - Number Theory Objectives

Number theory questions are represented on the *Number Sense and Operations* content domain of the NES Middle Grades Math examination. Demonstrate your proficiency at applying these concepts as they relate to prime factorization, the greatest common factor and the least common multiple. The *Number Sense and Operations* domain is the first of four examination domains, and it accounts for 17% of the test score. Provide accurate answers to the examination's 150 multiple-choice questions in order to qualify for a middle grades mathematics teaching certification. This computer-based assessment should take no longer than four hours and 15 minutes to finish.

### 1. What Are Prime Numbers? - Definition & Examples

In this lesson, we'll do a brief review of factors, and then learn how factors make prime numbers unique. You can also test your knowledge with a brief quiz.

### 2. What Are Composite Numbers? - Definition & Examples

In this lesson, you'll learn what composite numbers are and briefly touch on prime numbers. You'll also learn a couple of rules about composite numbers. Then, you can test your new knowledge with a brief quiz.

### 3. What Are Odd & Even Numbers? - Definition & Examples

In this lesson, you'll learn what odd and even numbers are with the help of some visual aids. You'll also learn some interesting properties of odd and even numbers. Then, you can test your new knowledge with a brief quiz.

### 4. How to Find the Prime Factorization of a Number

The prime factorization of a number involves breaking that number down to its smallest parts. This lesson will show you two different ways to discover the prime factorization of any number.

### 5. Finding the Prime Factorization with Exponents

After watching this video lesson, you will be able to factor any number using just prime numbers and exponents. Learn how to break apart any number you are given. Then, test your new knowledge with some examples.

### 6. How to Find the Greatest Common Factor

If the factors of a number are the different numbers that you can multiply together to get that original number, then the greatest common factor of two numbers is just the biggest one that both have in common. See some examples of what I'm talking about here!

### 7. How to Find the Least Common Multiple

The least common multiple of two numbers is the smallest number that can be divided evenly by your two original numbers. See some examples of what I'm talking about here!

### 8. Using Prime Factorizations to Find the Least Common Multiples

Finding the least common multiple can seem like a lot of work. But we can use prime factorization as a shortcut. Find out how and practice finding least common multiples in this lesson.

### 9. Word Problems: Greatest Common Factor & Least Common Multiple

In this video lesson, you will learn what kinds of word problems you can expect to see that involve the greatest common factor or the least common multiple. Learn what you need to do to understand these problems and then to solve them.

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### Other Chapters

Other chapters within the NES Middle Grades Mathematics (203): Practice & Study Guide course

- NES Middle Grades Math: Basic Arithmetic Operations
- NES Middle Grades Math: Solving Word Problems
- NES Middle Grades Math: Properties of Numbers
- NES Middle Grades Math: Estimating & Rounding
- NES Middle Grades Math: Roots & Radical Expressions
- NES Middle Grades Math: Exponents & Exponential Expressions
- NES Middle Grades Math: Scientific Notation
- NES Middle Grades Math: Simplifying Expressions
- NES Middle Grades Math: Integers
- NES Middle Grades Math: Rational Numbers
- NES Middle Grades Math: Introduction to Fractions
- NES Middle Grades Math: Operations with Fractions
- NES Middle Grades Math: Introduction to Decimals
- NES Middle Grades Math: Operations with Decimals
- NES Middle Grades Math: Percents
- NES Middle Grades Math: Money & Consumer Math
- NES Middle Grades Math: Number Patterns & Sequences
- NES Middle Grades Math: Properties of Functions
- NES Middle Grades Math: Graphing Functions
- NES Middle Grades Math: Negative Numbers
- NES Middle Grades Math: Absolute Value
- NES Middle Grades Math: Inequalities
- NES Middle Grades Math: Factoring
- NES Middle Grades Math: Monomials & Polynomials
- NES Middle Grades Math: Writing Algebraic Expressions
- NES Middle Grades Math: Basic Algebraic Expressions
- NES Middle Grades Math: Algebraic Distribution
- NES Middle Grades Math: One-Step Equations
- NES Middle Grades Math: Two-Step Equations
- NES Middle Grades Math: Rational Expressions
- NES Middle Grades Math: The Coordinate Graph
- NES Middle Grades Math: Linear Equations
- NES Middle Grades Math: Systems of Linear Equations
- NES Middle Grades Math: Rates, Ratios & Proportions
- NES Middle Grades Math: Measurement
- NES Middle Grades Math: Perimeter & Area
- NES Middle Grades Math: Polyhedrons & Geometric Solids
- NES Middle Grades Math: Symmetry, Similarity & Congruence
- NES Middle Grades Math: Properties of Lines
- NES Middle Grades Math: Angles
- NES Middle Grades Math: Triangles
- NES Middle Grades Math: Triangle Theorems & Proofs
- NES Middle Grades Math: Similar Polygons
- NES Middle Grades Math: The Pythagorean Theorem
- NES Middle Grades Math: Quadrilaterals
- NES Middle Grades Math: Circles
- NES Middle Grades Math: Circular Arcs & Measurement
- NES Middle Grades Math: Transformations
- NES Middle Grades Math: Data & Graphs
- NES Middle Grades Math: Statistics
- NES Middle Grades Math: Data Collection
- NES Middle Grades Math: Samples & Populations
- NES Middle Grades Math: Probability
- NES Middle Grades Math: Sets
- NES Middle Grades Mathematics Flashcards