How to Find Prime Factors
Our prime factorization calculator breaks down any number into its prime factors. Essential for understanding number structure, finding GCD/LCM, and solving number theory problems.
Understanding Prime Factorization
Every integer greater than 1 can be expressed as a unique product of prime numbers. This is called the Fundamental Theorem of Arithmetic. Prime factors are the "building blocks" of all numbers.
Prime Factorization Method
Divide by the smallest prime (2) as many times as possible, then 3, then 5, and continue with primes until the quotient is 1. Record each prime divisor.
Example:
60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5 = 2² × 3 × 5. Check: 4 × 3 × 5 = 60 ✓
Common Use Cases
Real-world applications for this calculator
Finding GCD/LCM
Compare prime factors to find common divisors or multiples.
Cryptography
Large primes are used in encryption algorithms like RSA.
Simplifying Radicals
Factor to simplify square roots and other radicals.
Tips
- Start with 2 (the only even prime) and work up.
- You only need to test primes up to √n.
- Every even number > 2 has 2 as a factor.
- Write answers in exponential form: 72 = 2³ × 3².
Frequently Asked Questions
What is a prime number?
A prime number has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13. Note that 1 is not prime (it has only one factor).
How do I find prime factors?
Start dividing by 2 repeatedly until odd, then try 3, 5, 7, etc. Each time you successfully divide, write down that prime. Continue until the result is 1.
Is prime factorization unique?
Yes! The Fundamental Theorem of Arithmetic states every integer > 1 has a unique prime factorization (ignoring order). 12 is always 2² × 3.
How do I use prime factors to find GCD?
Factor both numbers. GCD uses the shared primes with the lowest exponents. GCD(24, 36): 24 = 2³ × 3, 36 = 2² × 3². GCD = 2² × 3 = 12.
What is the largest known prime?
As of 2024, it's 2^82,589,933 − 1, a Mersenne prime with over 24 million digits. New largest primes are discovered periodically.