Prime Factorization Calculator
Break a number into prime factors, check if it's prime, and list its divisors
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Quick summary
Enter a whole number to see its prime factorization — the primes that multiply to make it, in exponent form. 12 = 2² × 3, and 100 = 2² × 5². The tool also tells you whether the number is prime (17 is; it has only 1 and itself as divisors) and lists all its divisors. Prime factorization is the foundation for GCDs, LCMs, and reducing fractions.
Reviewed by Simple Calculators TeamLast reviewed
How to use this calculator
- Enter the inputs requested by the calculator.
- Choose the units or options that match your situation and review the assumptions.
- Run or update the calculation to see the result.
- Review the result, breakdown, and formulas shown on the page.
- Check the inputs, units, dates, and limitations before saving or sharing the result.
Frequently asked questions
What is prime factorization?
Prime factorization expresses a number as a product of prime numbers — the unique set of primes that multiply to make it. For 12, that's 2 × 2 × 3, written 2² × 3. Every whole number greater than 1 has exactly one prime factorization (the fundamental theorem of arithmetic).
How do I find prime factors?
Divide the number by the smallest prime that goes in evenly (2, then 3, 5, 7…), repeating with each quotient until you reach 1. For 12: 12 ÷ 2 = 6, 6 ÷ 2 = 3, 3 ÷ 3 = 1, giving 2 × 2 × 3. This calculator does the division and groups repeats into exponents.
How do I know if a number is prime?
A prime number has exactly two divisors: 1 and itself. If its only prime factor is the number itself, it's prime — like 17. The calculator flags primes directly and shows their two divisors.
What is prime factorization used for?
It's the basis for finding the greatest common divisor and least common multiple, reducing fractions to lowest terms, and simplifying radicals. It's also central to number theory and underlies modern cryptography, which relies on the difficulty of factoring very large numbers.
Key terms
- Prime Number
- A number greater than 1 divisible only by 1 and itself.
- Prime Factor
- A prime that divides the number evenly.
- Divisor
- Any number that divides the target with no remainder.
- Exponent Form
- Repeated primes written compactly, e.g. 2² × 3.
Methodology, sources & limitations
This page shows the formula, assumptions, and limitations used for this estimate. Rates, thresholds, and other time-sensitive inputs can change, so verify them against the relevant official source before relying on a result.
For our review approach and the primary sources we consult, see the methodology and source policy. If you spot an outdated figure or formula, please contact us with a correction.