1. What Are Prime Factors?

Prime factors are the prime numbers that multiply together to give the original number. Every integer greater than 1 is either a prime number or can be expressed as a unique product of prime numbers (Fundamental Theorem of Arithmetic).

2. How Prime Factorization Works

The calculator uses the division method:

Step-by-step process:

• Start with the smallest prime number (2)
• Divide the number by this prime as many times as possible
• Move to the next prime number (3, 5, 7, etc.)
• Continue until the quotient becomes 1
• All divisors used are the prime factors

Example: 60 = 2 × 2 × 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 the prime factors in multiplication form. If the number is prime, it will be indicated as such.

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: Why is 1 not a prime number?
A: By definition, prime numbers must have exactly two distinct positive divisors. 1 has only one divisor (itself), so it's not considered prime.

Q3: Can prime factorization be done for negative numbers?
A: Prime factorization is typically defined for positive integers greater than 1. Negative numbers can be factored by including -1 as a factor.

Q4: What is the largest known prime number?
A: As of 2024, the largest known prime is 2^82,589,933 − 1, a number with 24,862,048 digits.

Q5: How is prime factorization used in cryptography?
A: RSA encryption relies on the difficulty of factoring large numbers into their prime components, which forms the basis of secure digital communication.