CalKit

Prime Factorization Calculator

Find the prime factorization of a natural number.

소인수분해
합성수
2³ × 3² × 5

소인수분해 결과

입력360
소인수분해360 = 2³ × 3² × 5
소인수 목록2, 3, 5
소수 여부소수가 아닙니다
약수의 개수24개
약수 목록1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

인수분해 트리

360
├─ 2 (소수)
└─ 180
   180
   ├─ 2 (소수)
   └─ 90
      90
      ├─ 2 (소수)
      └─ 45
         45
         ├─ 3 (소수)
         └─ 15
            15
            ├─ 3 (소수)
            └─ 5
               5 (소수)

Overview

The Prime Factorization Calculator breaks down a natural number into its prime factors. Prime factorization is fundamental for finding divisors, computing GCD/LCM, and is even used in cryptography.

Formula

Prime factorization: N = p₁^a₁ × p₂^a₂ × ... × pₖ^aₖ (p = prime, a = exponent)

Example: 360 = 2³ × 3² × 5¹

Number of divisors: (a₁+1)(a₂+1)...(aₖ+1)
Sum of divisors: Π(pᵢ^(aᵢ+1) - 1) / (pᵢ - 1)

How to Use

  1. 1Enter a natural number of 2 or greater.
  2. 2The prime factorization result is displayed in exponent form.
  3. 3The number of divisors and a list of all divisors are also shown.

Tips

  • ✔Start dividing from the smallest prime (2) for efficiency.
  • ✔You only need to check up to √N to find all prime factors.
  • ✔Knowing the prime factorization lets you compute the number of divisors using a formula.

FAQ

Q. What is a prime number?

A natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13, ... Note that 2 is the only even prime.

Q. Why is 1 not a prime number?

To guarantee the uniqueness of prime factorization (the Fundamental Theorem of Arithmetic). If 1 were prime, 6 = 2×3 = 1×2×3 = 1×1×2×3, making factorization non-unique.

Q. Where is prime factorization used?

GCD/LCM calculations, finding divisors, simplifying fractions, and RSA encryption (which relies on the difficulty of factoring large numbers). It plays a crucial role in computer security.

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