🎓 Mathematics • Number Theory
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Prime Factorization Calculator
Decomposes integers into canonical prime factors (n = p₁^a₁ · p₂^a₂), listing all divisors and factor pairs.
Fractions & Number Theory
Fractions, Primes & Factors Studio
Precision fraction reduction to lowest terms, primality tests, Sieve of Eratosthenes generator, divisor sums, and Euclidean GCD/LCM steps.
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Interesting Examples:
Number Classification
Abundant Number
Sum of proper divisors = 810 (compared to N = 360)
Total Divisors σ₀(N)24
Divisor Sum σ₁(N)1170
Proper Sum810
All Divisors of 360
1234568910121518202430364045607290120180360
What is Prime Factorization?
Expresses a composite number as a unique product of prime numbers, known as its prime factorization.
Formula & Step-by-Step Calculation
n = p₁^a₁ × p₂^a₂ × ... × pₖ^aₖ
Unique prime factorization by the Fundamental Theorem of Arithmetic.
Worked Step-by-Step Examples
Example 1
Prime factors of 360
Solution: 2³ × 3² × 5
• 360 = 2 × 180 = 2² × 90 = 2³ × 45 = 2³ × 3² × 5
Common Real-World & Academic Use Cases
- ✓ Simplifying square roots
- ✓ RSA encryption key factoring
- ✓ Divisor count calculation
How to Use the Prime Factorization Calculator
1
Enter Integer
Input number.
2
Inspect Prime Powers
View exponential prime factor breakdown.
Frequently Asked Questions
Q: What is the Fundamental Theorem of Arithmetic?
Every integer greater than 1 is either prime or can be uniquely factored into prime numbers.