Prime Factorization Calculator
Factor one number or a whole list at once. Get the exponent form, expanded product, distinct primes, divisor count, and a factor tree, all in your browser.
- Free, no account
- No watermark
- No usage limit
About the Prime Factorization Calculator
Type one whole number and this prime factorization calculator breaks it into the primes that multiply to make it. Enter 360 and you get 2 × 2 × 2 × 3 × 3 × 5, gathered into 2³ × 3² × 5, plus the distinct primes, the divisor count, and a factor tree like the one you'd draw on paper.
Paste a whole list of numbers, one per line, and it factors every single one in the same instant. Most free factorization tools handle exactly one number per click. If a homework page has twenty numbers to break down, you're stuck typing, hitting calculate, copying the answer, clearing the box, and starting over, twenty times. Here you paste the whole column once, get twenty factorizations back, then copy them all or pull them into a spreadsheet as a CSV. It runs in your browser, nothing gets uploaded, and there's no sign-up.
How to use it
- Type a number in the box, anything from 2 up to the 10¹⁵ cap. The full breakdown appears as you type, no button to press.
- Or paste a list. Put one number per line (commas and spaces work too) and each gets its own factorization. You can also drag a .txt or .csv file onto the box, or paste a column straight from a spreadsheet.
- Read the exponent form for a single number, the compact
2³ × 3² × 5answer, with the expanded product and distinct primes underneath. - Copy your results. A single number has a Copy button. A list gives you Copy all and Download .csv, and the CSV opens cleanly in Excel or Sheets with a column for each view: exponent form, expanded product, distinct primes, and divisor count.
- Share the exact list. The Share button builds a link that reopens the same numbers, so a saved worksheet is one bookmark away.
Enter a prime and the tool tells you it's prime and stops, since a prime has no smaller factors. Feed it 0, 1, a negative, or a decimal and you get a short plain explanation for that entry instead of a broken result. In a batch, bad entries are marked skipped and the good ones still come through.
Factoring a whole list at once
This is the feature to reach for when the numbers pile up. A teacher building an answer key, a student checking a page of problems, anyone reducing a stack of fractions, they all hit the same wall on other tools: one number at a time.
Paste this straight in:
84
90
360
1024
997
Each factorization comes back on its own row (997 shows up as prime, because it is), with a running count of how many you factored. Hit Copy all for a clean text block, one line per number, or Download .csv to keep the columns and open them straight in a spreadsheet.
The cap is 1,000 numbers per batch, far more than any worksheet, and it keeps the whole thing quick even on a phone.
The four views, and the one people miss
For a single number you get four views of the same answer, each for a different job.
The exponent form (2³ × 3² × 5) is the compact version and the one you actually compute with. The expanded product (2 × 2 × 2 × 3 × 3 × 5) spells out every prime, which is often exactly what an answer key wants. The distinct primes list strips the repeats when you only care which primes are involved, not how many of each.
The fourth one is the divisor count, and it's the view most calculators leave out. Take the exponents in 2³ × 3² × 5, add 1 to each to get 4, 3, and 2, then multiply: 4 × 3 × 2 = 24. So 360 has exactly 24 divisors, and you never had to list a single one. That shortcut falls right out of the factorization, and it's handy once you're past the basics.
Where the factorization pays off
Factoring is not only a classroom exercise. It underlies a lot of everyday math, and this is where the batch mode connects.
Reducing fractions and finding GCDs. To simplify 84/90, factor both, 2² × 3 × 7 over 2 × 3² × 5, cancel the shared primes (one 2 and one 3), and you're left with 14/15. Those shared primes are the greatest common divisor. Factor a whole column of numerators and denominators at once and the pattern jumps out. Or let the GCD & LCM calculator do the pairing for you.
Spotting perfect squares. A number is a perfect square exactly when every exponent in its factorization is even. 900 = 2² × 3² × 5², all even, so it's 30 squared. 360 has an odd exponent on the 2 and the 5, so it isn't one.
Why the input is capped. Finding the two primes behind a huge number is brutally hard once those primes get large, which is the whole basis of RSA encryption. This tool stops at 10¹⁵ because it's a learning and everyday-math helper, not a cryptographic factoring engine.
Why 1 and 0 don't factor
People trip on this one constantly. 1 is not prime, and it has no prime factorization. A prime needs exactly two divisors, 1 and itself, and the number 1 has only one. There's a deeper reason too: if 1 counted, you could pad any answer with as many 1s as you liked (60 = 2² × 3 × 5 = 1 × 2² × 3 × 5 and on forever), and the promise that every number has one and only one factorization would collapse. So 1 sits on its own, neither prime nor composite.
0 fails for a different reason. Every prime divides 0, so no finite product of primes ever lands on it. Factorization isn't defined there, and the tool says so rather than faking an answer.
Frequently asked questions
What's the largest number I can factor?
Each number is capped at 10¹⁵, a quadrillion. Anything inside that range resolves in a fraction of a second, even a large prime, which is the slowest case. Numbers above the cap are marked and skipped so the rest of your batch still goes through. The hundreds-of-digits numbers used in real cryptography are out of reach for any browser tool, that problem is hard on purpose.
Can it factor negative numbers or decimals?
Prime factorization is only defined for whole numbers greater than 1, so decimals and negatives don't factor directly. For a negative, drop the sign and factor the positive value, then carry the minus separately (-84 is -1 × 2² × 3 × 7). A decimal like 3.5 isn't a whole number, so there's nothing to break down. In a batch, entries like these get flagged and passed over.
How do I read the caret notation in the export, like 2^3?
The caret means "to the power of", so 2^3 is 2 × 2 × 2, the same value the on-screen 2³ shows. The CSV uses carets instead of raised digits so a factorization drops into a spreadsheet cell or a text file cleanly and stays searchable. So 2^3 × 3^2 × 5 is three 2s, two 3s, and one 5, multiplied together.
Why does it say a number is prime instead of factoring it?
Because a prime can't be broken down any further, that's the definition. Enter 997 and the tool reports that it's prime, since its only divisors are 1 and 997. The same holds for 2, 3, 5, 7, 11, and every other prime. If the result is just the number you typed with nothing smaller beneath it, you've confirmed a prime.
Can I paste a column straight from a spreadsheet?
Yes. Copy a column of numbers in Excel, Sheets, or Numbers and paste it into the box. Each cell lands on its own line and gets factored. You can also drag a saved .csv or .txt file onto the box. Non-numeric cells are ignored, so a stray header row is fine. A cell formatted as 1,200 factors as twelve hundred, so twenty rows come back as twenty rows rather than splitting into a handful of stray 1s and 200s.
Is my data private, and does it work offline?
Every calculation runs on your device. The numbers you type never leave the browser, nothing is uploaded, logged, or saved, and there's no account. Once the page has loaded it keeps working offline, so you can factor a worksheet on a plane as easily as at your desk.
How is this different from a prime number checker?
A checker answers one question, is this number prime, yes or no. This calculator assumes most inputs aren't prime and hands you the full breakdown: which primes, how many of each, the divisor count, and a factor tree. Reach for the prime number checker when you only need the verdict, this one when you need the factors.