Prime Factorization Calculator
Break down any number into its prime factors with step-by-step solutions and factor trees
Calculate Prime Factorization
Enter any positive integer up to 1,000,000
Quick Examples
First 25 Prime Numbers
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
Prime Facts
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Prime number: Only divisible by 1 and itself
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Fundamental theorem: Every integer has unique prime factorization
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Factor tree: Visual method to find prime factors
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Applications: Cryptography, GCD, LCM calculations
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Infinitely many: There are infinite prime numbers
Understanding Prime Factorization
What is Prime Factorization?
Prime factorization is the process of breaking down a composite number into its prime factors. Every positive integer greater than 1 can be expressed as a unique product of prime numbers.
The Factor Tree Method
Step 1: Start with your number
Choose any composite number to factor
Step 2: Find two factors
Divide by smallest prime that works
Step 3: Continue factoring
Repeat until all factors are prime
Why is Prime Factorization Important?
- • Number Theory: Fundamental theorem of arithmetic
- • Cryptography: RSA encryption relies on large primes
- • Mathematics: Finding GCD and LCM
- • Problem Solving: Simplifying fractions and expressions
- • Computer Science: Hash functions and algorithms
Common Prime Factorizations
12 = 2² × 3
18 = 2 × 3²
30 = 2 × 3 × 5
60 = 2² × 3 × 5
100 = 2² × 5²