# Ch 11: TExES Physics/Math 7-12: Number Theory

### About This Chapter

## TExES Physics - Math 7-12 - Number Theory - Chapter Summary

This chapter on number theory will remind you of techniques for solving mathematics equations. Through several examples, you'll be shown how to apply the rules of prime and composite numbers as well as the necessary steps for calculating the greatest common factors and least common multiples. In anticipation of passing the TExES Physics - Math 7-12 examination, you can also explore Fermat's Last Theorem along with the Fundamental Theorem of Algebra. Watch this chapter's online video lessons for help with:

- Exploring factors along with composite and prime numbers
- Teaching the basics of odd and even numbers
- Identifying a number's prime factorization
- Factoring numbers with exponents and prime numbers
- Finding the least common multiples through prime factorization, and solving related word problems
- Understanding modular arithmetic and Mersenne primes
- Interpreting Fermat's Last Theorem, the fundamental theorem of algebra and the fundamental theorem of calculus
- Providing examples of Euclidian algorithms

Available around the clock, these self-paced video lessons are presented online and are delivered by seasoned professional educators. Submit your questions to them via the Dashboard area of the lessons and receive personalized assistance. The lessons can be paused and watched again, and the self-assessment quizzes can be taken more than once. You might even print out your quiz results and accompanying worksheets so that you can study even more conveniently.

### TExES Physics - Math 7-12 - Number Theory Objectives

Domain I of the TExES Physics - Math 7-12 examination is titled Number Concepts. The domain is equal to 7% of the test, and it encompasses several topics, including number theory. Demonstrate your ability to apply relevant principles as you seek to qualify for a Texas teaching endorsement in mathematics and physics. You'll be granted up to five hours to answer 120 multiple-choice questions on the computer-administered examination.

### 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. 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.

### 7. 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.

### 8. Modular Arithmetic & Congruence Classes

Modular arithmetic revolves around remainders; we'll explore what this means in greater detail and learn how to recognize congruence classes. We'll also learn how to add, subtract, and multiply in modular arithmetic.

### 9. Perfect Numbers & Mersenne Primes

Although computers facilitate searches for prime numbers and perfect numbers, fundamental number theory is still very relevant. In this lesson we explore how a particular type of prime number, the Mersenne prime, relates to perfect numbers.

### 10. Fermat's Last Theorem: Definition & Example

Considered a mathematical mystery for hundreds of years, watch this video lesson to learn what Fermat's Last Theorem tells us and why mathematicians struggled for years to prove it true.

### 11. Fundamental Theorem of Algebra: Explanation and Example

In this lesson, you will learn what the Fundamental Theorem of Algebra says. You will also learn how to apply this theorem in determining solutions of polynomial functions.

### 12. The Fundamental Theorem of Calculus

The fundamental theorem of calculus is one of the most important equations in math. In this lesson we start to explore what the ubiquitous FTOC means as we careen down the road at 30 mph.

### 13. Euclidean Algorithm & Diophantine Equation: Examples & Solutions

Finding the greatest common divisor of two numbers is nicely accomplished using the Euclidean algorithm. In this lesson, we use this algorithm to explore solutions of Diophantine equations.

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### Other Chapters

Other chapters within the TExES Physics/Mathematics 7-12 (243): Practice & Study Guide course

- TExES Physics/Math 7-12: Teaching Math & Science
- TExES Physics/Math 7-12: Basic Arithmetic
- TExES Physics/Math 7-12: Real Numbers
- TExES Physics/Math 7-12: Decimals & Fractions
- TExES Physics/Math 7-12: Ratios, Percent & Proportions
- TExES Physics/Math 7-12: Exponents & Exponential Expressions
- TExES Physics/Math 7-12: Algebraic Expressions & Equations
- TExES Physics/Math 7-12: Rational Expressions
- TExES Physics/Math 7-12: Radical Expressions
- TExES Physics/Math 7-12: Complex & Imaginary Numbers
- TExES Physics/Math 7-12: Vector Operations
- TExES Physics/Math 7-12: Sequences & Series
- TExES Physics/Math 7-12: Functions
- TExES Physics/Math 7-12: Graphing & Functions
- TExES Physics/Math 7-12: Linear Equations
- TExES Physics/Math 7-12: Quadratic Equations
- TExES Physics/Math 7-12: Graphing & Factoring Quadratic Equations
- TExES Physics/Math 7-12: Matrices & Determinants
- TExES Physics/Math 7-12: Polynomials
- TExES Physics/Math 7-12: Exponential & Logarithmic Functions
- TExES Physics/Math 7-12: Trigonometry
- TExES Physics/Math 7-12: Continuity in Calculus
- TExES Physics/Math 7-12: Limits in Calculus
- TExES Physics/Math 7-12: Derivatives & Differentiation in Calculus
- TExES Physics/Math 7-12: Foundations of Geometry
- TExES Physics/Math 7-12: Geometry and Measurement
- TExES Physics/Math 7-12: Geometric Figures
- TExES Physics/Math 7-12: Parallel Lines & Polygons
- TExES Physics/Math 7-12: Properties of Triangles
- TExES Physics/Math 7-12: Geometric Solids
- TExES Physics/Math 7-12: Analytical Geometry
- TExES Physics/Math 7-12: Similar Polygons
- TExES Physics/Math 7-12: Conic Sections
- TExES Physics/Math 7-12: Circular Arcs & Circles
- TExES Physics/Math 7-12: Triangle Theorems & Proofs
- TExES Physics/Math 7-12: Statistics
- TExES Physics/Math 7-12: Probability
- TExES Physics/Math 7-12: Discrete Probability Distributions
- TExES Physics/Math 7-12: Continuous Probability Distributions
- TExES Physics/Math 7-12: Statistical Inference
- TExES Physics/Math 7-12: Mathematical Reasoning
- TExES Physics/Math 7-12: Applied Math
- TExES Physics/Math 7-12: Scientific Inquiry & Process
- TExES Physics/Math 7-12: Vectors & Scalars
- TExES Physics/Math 7-12: Kinematics
- TExES Physics/Math 7-12: Motion
- TExES Physics/Math 7-12: Fluid Mechanics
- TExES Physics/Math 7-12: Linear Momentum
- TExES Physics/Math 7-12: Work, Energy & Power
- TExES Physics/Math 7-12: Laws of Gravitation
- TExES Physics/Math 7-12: Oscillations
- TExES Physics/Math 7-12: Rotational Motion & Conservation of Energy
- TExES Physics/Math 7-12: Heat & Energy
- TExES Physics/Math 7-12: Thermodynamics
- TExES Physics/Math 7-12: Electrical Forces & Fields
- TExES Physics/Math 7-12: Potential & Capacitance
- TExES Physics/Math 7-12: Current Circuits
- TExES Physics/Math 7-12: Magnetism
- TExES Physics/Math 7-12: Waves, Sound & Light
- TExES Physics/Math 7-12: Quantum Physics
- TExES Physics/Mathematics 7-12 Flashcards