1. What Are Prime Factors?

Prime factors are the prime numbers that divide a given number exactly, without leaving a remainder. Every composite number can be expressed as a unique product of prime factors.

2. How Prime Factorization Works

The calculator uses the division method for prime factorization:

Process:

• Divide the number by the smallest prime number (2)
• Continue dividing the quotient by prime numbers
• Repeat until the quotient becomes 1
• All divisors used are the prime factors

Example: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5

3. Importance of Prime Factorization

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

4. Using the Calculator

Instructions: Enter any integer greater than 1. The calculator will display both the complete prime factorization and the list of unique prime factors.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between factors and prime factors?
A: Factors are all numbers that divide evenly, while prime factors are only the prime numbers among those factors.

Q2: Why is 1 not considered a prime number?
A: 1 only has one positive divisor (itself), while prime numbers must have exactly two distinct positive divisors.

Q3: Can prime factorization be done for prime numbers?
A: Yes, the prime factorization of a prime number is the number itself (e.g., 17 = 17).

Q4: What is the Fundamental Theorem of Arithmetic?
A: It states that every integer greater than 1 has a unique prime factorization, regardless of the order of factors.

Q5: How is prime factorization used in cryptography?
A: RSA encryption relies on the difficulty of factoring large composite numbers into their prime factors.