Prime Factorization Calculator
Find all prime factors of any number. Get results in expanded and exponential form with step-by-step solutions.
About Prime Factorization
What is Prime Factorization?
Prime factorization is the process of expressing a number as a product of its prime factors. Every integer greater than 1 can be uniquely represented as a product of prime numbers (Fundamental Theorem of Arithmetic).
First 25 Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
- 2 is the only even prime number
- 1 is NOT a prime number
- Prime numbers are infinite
- Every composite number has unique prime factorization
Methods Used
- Trial Division: Divide by smallest primes until quotient reaches 1
- Factor Tree: Visual breakdown showing each division step
- Exponential Form: Compact notation showing repeated factors as powers
Applications of Prime Factorization
- Finding GCF & LCM: Essential for fraction operations
- Simplifying Fractions: Cancel common factors
- Square Roots: Simplify √n by taking half of exponents
- Perfect Squares: All even exponents = perfect square
- Cryptography: Basis for encryption algorithms
Tips
- Always verify by multiplying factors back
- Use exponential form for large numbers
- Factor count = product of (exponent + 1) for each prime
- Prime numbers have exactly 2 factors: 1 and themselves
About This Calculator
Frequently Asked Questions
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