Prime Factorization Calculator
Decompose any number into its prime factors
Prime Factorization Calculator
Use our prime factorization calculator to decompose any positive integer into its prime factors. View the step-by-step factorization process, factor tree, and prime factor frequency table.
🔍 Prime Factorization Calculator
Quick Examples
📊 Results
Prime Factor Table
| Prime Factor | Exponent | Value |
|---|
Factor Tree
📝 Step-by-Step Division
📚 Understanding Prime Factorization
What is Prime Factorization?
Prime factorization is the process of decomposing a composite number into a product of prime numbers. Every integer greater than 1 either is a prime itself or can be represented as a unique product of prime numbers. This is known as the Fundamental Theorem of Arithmetic.
What is a Prime Number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31... The number 2 is the only even prime number.
How to Find Prime Factors
Start dividing the number by the smallest prime (2). Keep dividing by 2 until it's no longer divisible. Then try the next prime (3), then 5, 7, and so on. Continue until the quotient becomes 1. The divisors used are the prime factors.
Applications of Prime Factorization
- Finding GCF and LCM: Prime factorization is the most reliable method to find the greatest common factor and least common multiple of two or more numbers.
- Simplifying Fractions: Use prime factors to find common factors and reduce fractions to their simplest form.
- Cryptography: RSA encryption relies on the difficulty of factoring very large numbers into their prime components.
- Number Theory: Prime factorization is fundamental to understanding divisibility, modular arithmetic, and many other mathematical concepts.
- Perfect Numbers: Understanding prime factors helps identify perfect numbers and Mersenne primes.
Common Examples
| Number | Prime Factorization | Exponential Form |
|---|---|---|
| 12 | 2 × 2 × 3 | 2² × 3 |
| 36 | 2 × 2 × 3 × 3 | 2² × 3² |
| 60 | 2 × 2 × 3 × 5 | 2² × 3 × 5 |
| 100 | 2 × 2 × 5 × 5 | 2² × 5² |
| 360 | 2 × 2 × 2 × 3 × 3 × 5 | 2³ × 3² × 5 |