Factor a composite number
3602^3 x 3^2 x 5
Prime Factorization Calculator
Use this free prime factorization calculator to rewrite a positive whole number as prime factors, group repeated factors as exponents, count factors, list factor pairs, and check whether the number is prime or composite.
Prime factorsPower formPrime checkCopy results
6 prime factors2^3 x 3^2 x 5
- Factor count
- 24
- Factor pairs
- 12
- Prime factors
- 2^3 x 3^2 x 5
Steps
- Start with 360 and try the smallest prime factor first.
- Divide by that prime until it no longer divides evenly, then move to the next prime.
- Group repeated primes as powers: 2^3 x 3^2 x 5.
- As a check, multiply the prime factors back to get 360.
Recent answers
Recent prime factorizations will appear here.
Input tips
Enter one positive whole number up to 1,000,000,000,000.
The tool rewrites it as prime numbers multiplied together.
How to use the Prime Factorization Calculator
- Enter one positive whole number.
- Press Factor into primes to break it into prime factors.
- Review repeated prime factors as exponents and check whether the number is prime.
- Use examples, recent answers, or copy the result while checking factorization work.
What people use it for
Rewrite a number as prime factors for homework, notes, or answer checks.
Check whether a positive whole number is prime or composite before moving on.
Use prime powers before finding GCF, LCM, simplifying fractions, or comparing ratios.
Compare prime factorization with the full factor count and factor pairs.
Quick examples
Check a prime number
99739973 is prime
Break down a highly composite number
50402^4 x 3^2 x 5 x 7
See repeated factors as powers
10242^10
Factor a smaller classroom number
842^2 x 3 x 7
Check a number with a larger prime factor
9993^3 x 37
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Prime Factorization CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- CalculatorsBrowse related calculators and utilities in the same category.
- Calculator and utility guidesFind more guides that use real tool inputs and example numbers.
- All free toolsSearch every live tool, converter, calculator, AI helper, and browser utility.
Frequently asked questions
Quick answers about prime factors, repeated factors, exponents, prime checks, input limits, and privacy.
What does prime factorization mean?
Prime factorization rewrites a whole number as prime numbers multiplied together. For example, 360 becomes 2^3 x 3^2 x 5.
What is a prime number?
A prime number is a whole number greater than 1 with exactly two positive factors: 1 and itself.
What do the main Prime Factorization Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Prime Factorization Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
Why do repeated prime factors become exponents?
Exponents keep repeated factors short. Instead of writing 2 x 2 x 2, the calculator writes 2^3.
How is this different from the Factor Calculator?
The Factor Calculator lists every factor and factor pair. This calculator focuses on the prime factors that multiply back to the original number.
What does the calculator show for 1?
The number 1 has no prime factorization because it is not prime and not composite. The calculator will say that directly instead of forcing a fake prime factor.
How do I check the prime factorization?
Multiply the prime powers back together. For 360, 2^3 x 3^2 x 5 means 8 x 9 x 5, which equals 360.
Why are factor count and factor pairs shown?
They help you cross-check the result. Prime factorization explains the building blocks, while factor count and factor pairs show how many whole-number divisors the number has.
Can I enter decimals or negative numbers?
No. This tool is for positive whole numbers. Decimals, fractions, negative values, zero, and Infinity are rejected so the result stays clear.
How does prime factorization help with GCF and LCM?
For GCF, compare the shared prime powers. For LCM, combine the highest needed prime powers. This is why prime factors are useful before GCF and LCM work.
What numbers can I enter?
Enter one positive safe whole number up to 1,000,000,000,000. Very large factorization can be slow, so this browser calculator keeps a practical limit.
What should I double-check before copying the answer?
Check that the input was a whole number, the prime factors multiply back to the original number, and any exponent form matches the repeated factors.
Is my number sent to a server?
No. The calculation runs in your browser tab and recent answers stay only in that tab while you use the page.