🔍 Prime Factorization Calculator
Find the prime factors of any number, check if a number is prime, and see the factor tree.
Enter a Number
Prime Factorization
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Is Prime?
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Number of Factors
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All Factors
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Sum of Factors
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What is Prime Factorization?
Prime factorization expresses a number as a product of its prime factors. Every integer greater than 1 is either prime itself or can be uniquely expressed as a product of primes (Fundamental Theorem of Arithmetic).
Example: 360 = 2³ × 3² × 5
= 2 × 2 × 2 × 3 × 3 × 5
= 2 × 2 × 2 × 3 × 3 × 5
Applications
- Finding GCF and LCM
- Simplifying fractions
- Cryptography (RSA encryption relies on difficulty of factoring large numbers)
- Solving Diophantine equations
What is a prime number? +
A prime number is a natural number greater than 1 with no positive divisors other than 1 and itself. The first primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29... There are infinitely many primes (proved by Euclid ~300 BC). The largest known prime as of 2024 has over 41 million digits.