1. What Is Prime Factorization?

Prime factorization is the process of determining which prime numbers multiply together to create the original number. Every integer greater than 1 is either a prime number or can be represented as a unique product of prime numbers.

2. How Prime Factorization Works

The calculator uses trial division to find prime factors:

Where:

• \( N \) — The original number to factor
• \( p_1, p_2, \ldots, p_n \) — Distinct prime factors
• \( k_1, k_2, \ldots, k_n \) — Their respective exponents

Example: 60 = 2² × 3 × 5

3. Importance of Prime Factorization

Applications: Prime factorization is fundamental in number theory, cryptography (RSA algorithm), finding greatest common divisors, and simplifying fractions.

4. Using the Calculator

Instructions: Enter any integer 2 or greater. The calculator will display its prime factors in exponential form.

5. Frequently Asked Questions (FAQ)

Q1: What is a prime number?
A: A natural number greater than 1 that has no positive divisors other than 1 and itself.

Q2: Is prime factorization unique?
A: Yes, according to the Fundamental Theorem of Arithmetic, every integer has a unique prime factorization (up to ordering).

Q3: How does this calculator handle large numbers?
A: It uses efficient trial division but may be slow for very large numbers (over 10 digits).

Q4: What's the complexity of this algorithm?
A: Trial division has O(√n) time complexity in the worst case.

Q5: Can 1 be prime factorized?
A: No, 1 is neither prime nor composite. The calculator requires input ≥ 2.