Prime Factorization Calculator
Break a whole number down into its prime factors.
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- Accurate results
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Enter a whole number to find its prime factorization.
Your result
2^3 × 3^2 × 5
Prime factorization
Distinct prime factors2, 3, 5
AI explanation
Formula
Repeatedly divides by the smallest possible prime until only 1 remainsWorked example
Prime factorization of 360
| Field | Value |
|---|---|
| Number | 360 |
| Prime factorization | 2^3 × 3^2 × 5 |
| Distinct prime factors | 2, 3, 5 |
Assumptions
- Every whole number greater than 1 has a unique prime factorization (the Fundamental Theorem of Arithmetic).
Frequently asked questions
What is prime factorization?
Expressing a number as a product of prime numbers — the "building blocks" that multiply together to make the original number.
Why is every number's prime factorization unique?
This is the Fundamental Theorem of Arithmetic — every integer greater than 1 can be written as a product of primes in exactly one way (ignoring the order of factors).
How is this used in practice?
Prime factorization is the basis for finding GCF and LCM by hand, and underlies cryptographic algorithms that rely on the difficulty of factoring very large numbers.