1 Integers The Basics

1.1 Introduction

1.2 Making Integers Out of Integers

1.3 Integer Multiples

1.4 Divisibility of Integers

1.5 Divisors

1.6 Using Divisors

1.7 Mathematical Symbols

1.8 Summary

2 Primes and Composites

2.1 Introduction

2.2 Primes and Composites

2.3 Identifying Primes I

2.4 Identifying Primes II

2.5 Summary

3 Multiples and Divisors

3.1 Introduction

3.2 Common Divisors

3.3 Greatest Common Divisors

3.4 Common Multiples

3.5 Remainders

3.6 Multiples, Divisors, and Arithmetic

3.7 The Euclidean Algorithm

3.8 Summary

4 Prime Factorization

4.1 Introduction

4.2 Factor Trees

4.3 Factorization and Multiples

4.4 Factorization and Dibisors

4.5 Rational Numbers and Lowest Terms

4.6 Prime Factorization and Problem Solving

4.7 Relationships Between LCMs and GCDs

4.8 Summary

5 Divisor Problems

5.1 Introduction

5.2 Counting Divisors

5.3 Divisor Counting Problems

5.4 Divisor Products

5.5 Summary

6 Special Numbers

6.1 Introduction

6.2 Some Special Primes

6.3 Factorials, Exponents and Divisibility

6.4 Perfect Abundant and Deficient Numbers

6.5 Palindromes

6.6 Summary

7 Algebra With Integers

7.1 Introduction

7.2 Problems

7.3 Summary

8 Base Numbers

8.1 Introduction

8.2 Counting in Bundles

8.3 BaseNumbers

8.4 Base Number Digits

8.5 Converting Integers Between Bases

8.6 Unusual Base Number Problems

8.7 Summary

9 Base Number Arithmetic

9.1 Introduction

9.2 Base Number Addition

9.3 Base Number Subtraction

9.4 Base Number Multiplication

9.5 BaseNumber Division and Divisibility

9.6 Summary

10 Units Digits

10.1 Introduction

10.2 Units Digits in Arithmetic

10.3 Base Number Units Digits

10.4 Unit Digits Everywhere!

10.5 Summary

11 Decimals and Fractions

11.1 Introduction

11.2 Terminating Decimals

11.3 Repeating Decimals

11.4 Converting Decimals to Fractions

11.5 BaseNumbersandDecimaquivalents

11.6 Summary

12 Introduction toModular Arithmetic

12.1 Introduction

12.2 Congruence

12.3 Residues

12.4 Addition and Subtraction

12.5 Multiplication and Exponentiation

12.6 Patterns and Exploration

12.7 Summary

13 Divisibility Rules

13.1 Introduction

13.2 Divisibility Rules

13.3 Divisibility Rules With Algebra

13.4 Summary

14 Linear Congruences

14.1 Introduction

14.2 Modular Inverses and Simple Linear Congruences

14.3 Solving Linear Congruences

14.4 Systems of Linear Congruences

14.5 Summary

15 Number Sense

15.1 Introduction

15.2 Familiar Factors and Divisibility

15.3 Algebraic Methods of Arithmetic

15.4 Useful Forms of Numbers

15.5 Simplicity

15.6 Summary