1 is not prime
We keep 1 out of the prime club so every integer >1 has a unique prime factorization (the Fundamental Theorem of Arithmetic).
Definition choice
Prime Number Checker & Prime Factorization
Input & Actions
Tip: accepts integers like 84, -210, or big integers (within reason). Decimals are not supported.
Results will appear here.
About This Prime Factorization Calculator
Need to break a number into its building blocks? This calculator checks whether a number is prime and, if it is not, finds its prime factorization. Prime factorization is the process of writing a whole number as a product of prime numbers, and it is a core idea in math classes, number theory, and practical tasks like simplifying fractions. Instead of guessing and dividing by hand, you can enter a number and get a clean, readable result in seconds.
The concepts are simple. A prime number is greater than 1 and has no divisors other than 1 and itself. A composite number has at least one other divisor. Every whole number greater than 1 can be written as a product of primes in one and only one way (ignoring order). That is why prime factorization is so useful: once you have the prime factors, you can quickly find greatest common factors, least common multiples, and simplify ratios.
How to Use the Calculator
- Enter any whole number. Negative values are allowed and will be shown with a factor of -1.
- Click “Calculate” to see whether the number is prime or composite.
- Use “Show Steps” if you want to view the division process and intermediate factors.
- Click “Copy Result” to paste the factorization into homework, notes, or a worksheet.
- Use “Add Example” to try a sample input and see the formatting.
Here is a quick example. The number 84 is composite, and its prime factorization is 2 × 2 × 3 × 7, often written as 22 × 3 × 7. That makes it easy to simplify a fraction like 84/126 by canceling shared factors, or to compute the least common multiple of 84 and another number by combining prime powers.
This tool uses a fast, optimized trial division method. It checks small primes first and only tests divisors up to the square root of the number, which is enough to confirm primality. For typical classroom-sized inputs, results are nearly instant. Very large numbers can take longer, so if you are working with huge values, expect a brief pause.
Whether you are practicing for a math test, teaching factors and multiples, or just verifying a result, this prime factorization calculator gives a clear explanation and a dependable answer without manual trial and error.
FAQ
Is 1 prime?
No. By definition, primes are integers \(\ge 2\).
How are negatives handled?
We display \( -1 \times \) the factorization of \(|n|\). Example: \(-84 = -1 \times 2^2 \times 3 \times 7\).
Performance limits?
Trial division up to \( \sqrt{n} \) is quick for typical classroom sizes (up to ~1010 is usually fine in modern browsers). Extremely large inputs will take longer.
5 Fun Facts about Primes
2 is the only even prime
Every other even number has 2 as a factor, so 2 stands alone—making it both the smallest prime and the loneliest even one.
Even unicorn
Gaps can be huge
Primes get rarer but never stop. There are arbitrarily long stretches of composites—yet another prime always appears eventually.
Prime deserts
6k ± 1 shortcut
Every prime greater than 3 is of the form \(6k \pm 1\). That’s why this tool skips other residues when it searches.
Search trick
RSA leans on factoring
Modern encryption relies on the difficulty of factoring huge semiprimes. Fast factoring breaks keys—hence the race for quantum-safe crypto.
Crypto link