Theory of Positive Integers

An exploration of the properties, relationships, and applications of positive integers in various mathematical contexts.

Introduction to Positive IntegersDivisibility and MultiplesPrime Numbers and Composite Numbers
Greatest Common Divisor and Least Common MultipleThe Fundamental Theorem of ArithmeticNumber Patterns and Sequences
Using Positive Integers in Everyday LifePositive Integers in TechnologyOrganizing Events and Schedules
Breaking Down Problems with FactorizationUsing Patterns to Predict and Solve
Introduction to Posi...Divisibility and Mul...Prime Numbers and Co...Greatest Common Divi...The Fundamental Theo...Number Patterns and ...Using Positive Integ...Positive Integers in...Organizing Events an...Breaking Down Proble...Using Patterns to Pr...
Advanced Topics

The Fundamental Theorem of Arithmetic

What Does It Say?

Every positive integer greater than 1 can be written as a product of prime numbers, and this factorization is unique (except for the order).

Why Is It Awesome?

This theorem is like a "recipe" for building any number using primes, which are the basic "ingredients".

How Does It Work?

  • 30 = 2 × 3 × 5
  • 84 = 2 × 2 × 3 × 7

No matter how you factor, you'll always get the same prime numbers.

Uses in Math and Beyond

Prime factorization is important in cryptography, coding, and simplifying math problems!

Examples

  • The prime factorization of 60 is 2 × 2 × 3 × 5.

  • The prime factorization of 100 is 2 × 2 × 5 × 5.

In a Nutshell

Every number can be uniquely built from prime numbers, just like unique LEGO builds.

Next
Number Patterns and Sequences