Prime Factorization Calculator
Free prime factorization calculator. Break any number into its prime factors with a factor tree diagram and step-by-step working.
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Prime Factorization
Comprehensive Guide & Practice
Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.
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1. What Is Prime Factorization?
Prime factorization is the process of expressing a composite number as a product of its prime factors. Every integer greater than 1 is either prime itself or can be expressed uniquely as a product of primes — this is the Fundamental Theorem of Arithmetic.
For example: 360 = 2³ × 3² × 5 = 8 × 9 × 5 = 360.
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2. The Factor Tree Method
A factor tree is a visual diagram for finding prime factors:
- Start with the number (e.g. 36)
- Find any two factors: 36 = 6 × 6
- Keep breaking down composite factors: 6 = 2 × 3, 6 = 2 × 3
- Circle all prime numbers at the ends of branches: 2, 3, 2, 3
- Result: 36 = 2² × 3²
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3. Uses of Prime Factorization
- Finding GCF: The GCF of two numbers = product of all common prime factors at their lowest powers.
- Finding LCM: The LCM = product of all prime factors at their highest powers.
- Simplifying fractions: Divide numerator and denominator by their GCF.
- Cryptography: Modern encryption (RSA) relies on the difficulty of factoring very large numbers.
See also: LCM & GCF Calculator | Prime Number Checker | Prime Numbers Guide