Real Numbers: Prime Factorization

Discover the building blocks of all composite numbers through interactive visual exploration

Welcome back to the fascinating world of Real Numbers! Let's explore how every composite number can be broken down into prime building blocks.
📊 Real Numbers Review

Real numbers include both rational numbers (fractions like 1/2, 3/4) and irrational numbers (like √2, π) that fill the entire number line without gaps.

ℝ = ℚ ∪ (ℝ - ℚ)
Rationals + Irrationals = All Real Numbers
🔍 Prime Numbers

Prime numbers are the fundamental building blocks - numbers greater than 1 that can only be divided by 1 and themselves. They're like mathematical atoms!

2, 3, 5, 7, 11, 13, 17, 19, 23...
The building blocks of all numbers
🌳 Prime Factorization

Every composite number can be broken down into prime factors using factor trees. It's like finding the DNA of numbers!

32760 = 2³ × 3² × 5 × 7 × 13
Unique prime signature
🧩 Building Composites

Just as primes break numbers down, we can multiply primes together to build composite numbers. It's mathematical construction!

7 × 11 × 23 = 1771
Primes → Composite