Prime Factorization Calculator
Adjust the inputs below. Results update as you type.
How it works
Every integer > 1 is either prime or can be uniquely expressed as a product of primes (Fundamental Theorem of Arithmetic). Trial division: test primes 2, 3, 5, 7, ... up to √n. If none divide evenly, n is prime. Example: 360 = 2³ × 3² × 5. Used to find GCF, LCM, and simplify radicals. Large-number factorization is computationally hard—it underpins RSA encryption security.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Prime factorization breaks a number into the product of primes. Divide repeatedly by the smallest prime that fits until you reach 1.
Worked example
60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
What is prime factorization?+
Expressing a number as a product of prime numbers. Every integer above 1 has a unique prime factorization (the fundamental theorem of arithmetic).
How do I do it?+
Divide by the smallest prime that goes in evenly, then keep dividing the quotient until you reach 1, collecting the primes used.
Why is it useful?+
It underpins finding GCF and LCM, simplifying fractions, and much of number theory and cryptography.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.