Prime Factorization Calculator
Prime Factorization
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Number of Prime Factors
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Total Number of Divisors
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How Prime Factorization Works
Prime factorization breaks a number down into a product of prime numbers. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic). For example, 360 = 2^3 x 3^2 x 5.
The algorithm divides by the smallest prime (2) repeatedly, then tries 3, 5, 7, and so on up to the square root of the remaining number. If any number remains after this process, it must be prime itself.
Prime factorization is fundamental in number theory, cryptography (RSA encryption relies on the difficulty of factoring large numbers), and for finding GCD and LCM of numbers. It also determines the total count of divisors.
Frequently Asked Questions
Why is prime factorization unique?
The Fundamental Theorem of Arithmetic guarantees that every integer greater than 1 has exactly one prime factorization (up to ordering). This uniqueness is the foundation of many areas of mathematics.
How do you find the number of divisors?
From the prime factorization, if n = p1^a1 x p2^a2 x ... then the number of divisors is (a1+1)(a2+1)... For 360 = 2^3 x 3^2 x 5^1, divisors = 4 x 3 x 2 = 24.
What is the largest known prime number?
As of 2024, the largest known prime is 2^136,279,841 - 1, a Mersenne prime with over 41 million digits. Finding large primes is an active area of computational mathematics.