Prime Factorization Calculator
Enter any whole number up to 15 digits to see its prime factors, a factor tree, and its divisors.
All calculations run locally in your browser — nothing is uploaded.
How it works
- Type or paste a whole number (up to 15 digits) into the input field.
- Read the live results: prime factorization in exponent form, an ASCII factor tree, and a prime or composite verdict.
- Check the divisor section for the number of divisors, their sum, and — for numbers below 10,000 — the full divisor list.
Frequently asked questions
- How does this prime factorization calculator work?
- It uses trial division with a 2-3-5 wheel: after removing factors of 2, 3, and 5, it only tests candidate divisors that are coprime to 30, skipping about 73% of all numbers. Arithmetic runs on BigInt values, so every digit of a 15-digit input is handled exactly with no floating-point rounding.
- What is the largest number I can factor, and how fast is it?
- The input accepts up to 15 digits (just under one quadrillion). Numbers with small prime factors resolve almost instantly; the slowest cases are large primes or semiprimes with two big factors, which can take a few seconds while the calculator shows a working indicator. The work is chunked so the page stays responsive.
- Is the number I enter sent to a server?
- No. The entire computation runs in JavaScript inside your browser tab, and the page makes no network requests with your input. You can even load the page, disconnect from the internet, and keep factoring numbers.
- What does the exponent form of a factorization mean?
- Exponent form groups repeated prime factors, so 360 is written as 2³ × 3² × 5 instead of 2 × 2 × 2 × 3 × 3 × 5. This compact form is what the divisor formulas use: adding one to each exponent and multiplying gives the total number of divisors.
- Why does the divisor list only appear for numbers under 10,000?
- Small numbers have short, readable divisor lists, but large numbers can have tens of thousands of divisors, which would flood the page. For any input the calculator still reports the exact count of divisors and their exact sum, both derived directly from the prime factorization.
About this tool
This calculator breaks any whole number up to 15 digits into its prime factors — the unique set of primes that multiply together to produce it. Results update live as you type: you get the factorization in exponent form, a text factor tree that shows each split step by step, a clear prime-or-composite verdict, and divisor statistics. For numbers below 10,000 it also lists every divisor explicitly.
Under the hood the tool runs trial division on BigInt values, so 15-digit inputs are computed exactly rather than approximated with floating-point numbers. A wheel over the primes 2, 3, and 5 skips candidates divisible by any of them, cutting the work by nearly three quarters. Division only needs to be tested up to the square root of the remaining number, and the loop yields control periodically so your browser never freezes — a working indicator appears for hard cases such as large primes. Nothing you type leaves your device; there is no server-side processing at all.
Prime factorization sits underneath a surprising amount of everyday math. Students use it to find the greatest common divisor and least common multiple of two numbers, to simplify fractions and radicals, and to answer homework questions like how many divisors a number has. Programmers and puzzle solvers use it for modular arithmetic problems, hash table sizing, and Project Euler-style challenges. The divisor sum is also the quickest way to spot perfect numbers, where the sum of proper divisors equals the number itself.
A few practical tips: if a large input seems slow, it is usually because the number is prime or has two large prime factors — that is exactly the hard case, and the verdict at the end is still exact. To find the GCD of two numbers, factor each one and multiply the primes they share at the lowest exponent. And if you paste a number containing commas or spaces as thousands separators, the calculator strips them automatically.