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Prime Factorization Calculator

This powerful prime factorization calculator can decompose any positive integer into prime factors, providing complete calculation steps and visualization results. Perfect for learning, teaching, and solving mathematical problems.

Complete Prime Decomposition

Break down any integer into its prime factors with exponential notation and factor trees

Visual Factor Trees

Generate clear factor tree diagrams to visualize the decomposition process step by step

Educational Steps

Detailed mathematical explanations and step-by-step solutions for better understanding

Start Calculating

Enter your number and get complete prime factorization with visual trees

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What is Prime Factorization?

Understanding the foundation of number theory

Prime factorization is the process of expressing a positive integer as a product of prime numbers. Every integer greater than 1 can be uniquely represented as a product of primes (according to the Fundamental Theorem of Arithmetic).

Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. Examples include 2, 3, 5, 7, 11, 13, etc.

Key Properties

Every integer has a unique prime factorization
Prime factorization is the foundation of number theory
Used in cryptography and computer algorithms
Example: 60 = 2² × 3 × 5
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

Prime factors: 2, 2, 3, 5

Prime Factorization Examples

Common examples to understand the process

Here are some common examples of prime factorization:

12
2² × 3
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
28
2² × 7
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
45
3² × 5
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
72
2³ × 3²
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
100
2² × 5²
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
84
2² × 3 × 7
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

Frequently Asked Questions

Common questions about prime factorization

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