# Ch 7: SHSAT Math: Number Theory

### About This Chapter

## SHSAT Math: Number Theory - Chapter Summary

The lessons in this chapter can aid in your review of number theory as you study for the math segment of the SHSAT. Use our videos and quizzes to get information to answer questions on topics including:

- How to convert numbers to scientific notation
- Comparing numbers in scientific notation
- Characteristics of prime and composite numbers
- Prime factorization
- Determining greatest common factors and least common multiples

Our lessons are taught by professionals who understand the concepts you need to know for good performance on the SHSAT. You can contact them through our message board if you have questions. Lesson quizzes, chapter tests and a comprehensive final exam offer several opportunities to gauge your learning before test day. A clickable timeline in each lesson makes it easy to go back and review specific points without having to re-watch the entire video.

### SHSAT Math: Number Theory - Chapter Objectives

Taking the SHSAT is one of the requirements for applying to New York City's specialized high schools. There is a verbal portion and a math portion on the SHSAT. The math section contains 50 multiple-choice computation questions and word problems.

Because our lesson quizzes are also multiple choice, they provide good practice for this admissions test. You can assess your knowledge through our quizzes, and, if you miss an answer, use the links provided to jump back and review that part of the lesson.

### 1. Converting Numbers to Scientific Notation

After watching this video lesson, you will be able to convert any number you come across into scientific notation. You will also learn why scientific notation is used and where you are most likely to see it.

### 2. Comparing Numbers Written in Scientific Notation

After watching this video lesson, you will be able to compare numbers written in scientific notation with each other. You will learn how to tell which is larger and which is smaller.

### 3. Identifying Prime & Composite Numbers

In this video lesson, you will learn how to identify both prime and composite numbers. You will also learn what makes the numbers unique, as well as the characteristics of both these types of numbers.

### 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 SHSAT: Practice & Study Guide course

- Reading Comprehension Approaches
- Writing & Editing Written Work
- Practice Analyzing & Interpreting Texts
- SHSAT Math: Basic Arithmetic Operations
- SHSAT Math: Divisibility
- SHSAT Math: Number Properties
- SHSAT Math: Factoring
- SHSAT Math: Estimation & Rounding
- SHSAT Math: Whole Numbers
- SHSAT Math: Simplifying Expressions
- SHSAT Math: Negative Numbers
- SHSAT Math: Absolute Value
- SHSAT Math: Integers
- SHSAT Math: Rational Numbers
- SHSAT Math: Inequalities
- SHSAT Math: Operations with Decimals
- SHSAT Math: Introduction to Fractions
- SHSAT Math: Operations with Fractions
- SHSAT Math: Percents
- SHSAT Math: Exponents & Exponential Expressions
- SHSAT Math: Roots & Radical Expressions
- SHSAT Math: Basic Algebraic Expressions
- SHSAT Math: Algebraic Distribution
- SHSAT Math: Simplifying & Solving Rational Expressions
- SHSAT Math: The Coordinate Graph
- SHSAT Math: Linear Equations
- SHSAT Math: Systems of Linear Equations
- SHSAT Math: Properties of Functions
- SHSAT Math: Graphing Functions
- SHSAT Math: Solving Word Problems
- SHSAT Math: Introduction to Geometric Figures
- SHSAT Math: Triangles
- SHSAT Math: Quadrilaterals
- SHSAT Math: Circles
- SHSAT Math: Circular Arcs & Measurement
- SHSAT Math: Polyhedrons & Geometric Solids
- SHSAT Math: Symmetry, Similarity & Congruence
- SHSAT Math: Triangle Theorems & Proofs
- SHSAT Math: Similar Polygons
- SHSAT Math: The Pythagorean Theorem
- SHSAT Math: Units of Measurement
- SHSAT Math: Perimeter & Area
- SHSAT Math: Data & Graphs
- SHSAT Math: Probability
- SHSAT Math: Statistics
- SHSAT Math: Rates, Ratios & Proportions
- SHSAT Math: Consumer Math
- SHSAT Math: Number Sequences
- SHSAT Math: Sets & Subsets
- SHSAT Flashcards