1. What is Prime Factorization?

Prime factorization is the process of breaking down a composite number into the product of its prime factors. Every integer greater than 1 is either a prime number or can be written as a unique product of prime numbers.

2. How Does Prime Factorization Work?

The prime factorization of a number is expressed as:

Where:

• \( n \) — The composite number being factored
• \( p_1, p_2, \ldots, p_k \) — Prime factors
• \( e_1, e_2, \ldots, e_k \) — Exponents indicating the multiplicity of each prime factor

Explanation: The algorithm divides the number by the smallest prime factor repeatedly until the result becomes 1.

3. Importance of Prime Factorization

Details: Prime factorization is fundamental in number theory and has practical applications in cryptography, computer science algorithms, finding greatest common divisors, and simplifying fractions.

4. Using the Calculator

Tips: Enter any integer greater than 1. The calculator will display the prime factorization in exponential form. For example, 12 = 2² × 3.

5. Frequently Asked Questions (FAQ)

Q1: What is a prime number?
A: A prime number is 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 greater than 1 has a unique prime factorization.

Q3: What is the prime factorization of prime numbers?
A: Prime numbers are their own prime factorization. For example, the prime factorization of 7 is simply 7.

Q4: How does this calculator handle large numbers?
A: The calculator uses an efficient algorithm but may take longer for very large numbers (over 1,000,000).

Q5: What are some practical applications of prime factorization?
A: Prime factorization is used in RSA encryption, finding least common multiples, simplifying mathematical expressions, and various computer algorithms.