Number Theory
Explore factors, primes, and number properties
Topics
Factors & Multiples
GCF, LCM, and prime factorization
Divisibility
Divisibility rules and tests
Number Properties
Even, odd, and perfect squares
Number theory explores the fascinating properties and relationships of integers. Often called the "queen of mathematics," number theory investigates prime numbers, divisibility, factors, and patterns that have captivated mathematicians for millennia. These concepts form the foundation of modern cryptography and computer science.
In this category, you will discover the building blocks of our number system. You will learn about prime and composite numbers, find greatest common factors and least common multiples, and explore divisibility rules that make calculations easier. These concepts have practical applications in simplifying fractions, solving problems, and understanding mathematical structure.
Our lessons reveal the beauty and patterns hidden within numbers. You will use factor trees, Venn diagrams, and other visual tools to explore relationships. Whether you are building foundational skills or preparing for competition mathematics, number theory develops deep mathematical thinking.
What Students Will Learn
- Identify and generate prime and composite numbers
- Use divisibility rules for 2, 3, 4, 5, 6, 9, and 10
- Find all factors and factor pairs of numbers
- Calculate greatest common factor (GCF) using multiple methods
- Calculate least common multiple (LCM) efficiently
- Use prime factorization to solve problems
- Apply number theory concepts to simplify fractions and solve problems
Frequently Asked Questions
What is number theory?
Number theory studies properties of integers, especially prime numbers, divisibility, and factors. It is foundational for computer science and cryptography.
Why are prime numbers important?
Primes are the building blocks of all integers. They are essential for cryptography (secure internet), and their patterns remain one of mathematics greatest mysteries.
How is number theory used in real life?
Number theory underlies encryption for secure banking, messaging, and internet security. It is also used in coding theory, computer algorithms, and hash functions.