Prime Factorization Tool

📖 Introduction

Prime factorisation is a foundational skill in primary olympiad arithmetic and lower secondary number theory. Writing 360 as two cubed times three squared times five lets you count its divisors, work out greatest common divisors and least common multiples, and decide whether a number is prime. Enter any positive integer here and you immediately get the canonical factorisation with repeated primes collected into powers, the complete list of divisors, the divisor count and the divisor sum, plus a direct answer on whether the number is prime. Supply a second number and the tool also reports the greatest common divisor, the least common multiple and both factorisations side by side, which makes it obvious where a common divisor comes from. Tick the prime list option and the sieve of Eratosthenes generates every prime up to a limit you choose, together with the prime count and the twin prime pairs, supporting limits up to one hundred thousand. Everything is computed inside your browser with no network service involved, and large numbers you type in are never uploaded anywhere. The factorisation is presented in canonical form with repeated primes collected into powers, which is exactly the format expected in exam answers, and the divisor list is generated from the same prime decomposition so the two never disagree. Seeing the factorisations of two numbers side by side is the quickest way to understand why a greatest common divisor takes the lowest power of each shared prime while a least common multiple takes the highest. The prime table option turns the tool into a small sieve demonstrator: raise the limit and watch how the prime count grows, or scan the twin prime list to see pairs that differ by exactly two. Everything is computed locally, so even large limits stay responsive.

✨ Features

• Canonical prime factorisation with repeated primes automatically collected into powers.
• Lists every divisor together with the divisor count and the divisor sum.
• Tells you plainly whether the number is prime.
• With a second number, gives gcd, lcm and both factorisations for comparison.
• Generates a prime table by the sieve of Eratosthenes and counts primes and twin prime pairs.
• One-tap factorisation of common numbers such as 360, 1024, 97 and 1001.

🚀 How to use

1. Type the positive integer you want to factor into the first field.
2. When you need a gcd or lcm, type the other number into the second field.
3. Tick what you want to see: factorisation, divisor list, prime table, gcd and lcm.
4. Leaving the prime limit empty defaults to one hundred; the maximum is one hundred thousand.
5. Press the example button to load the classic pair 360 and 48.

⚠️ Notes

• Input range. Values up to one trillion are recommended; larger ones factor slowly and may freeze the page.
• Negatives and decimals. Only integers of two or above are handled; anything else triggers a message.
• Divisor display. When there are more than sixty divisors only the first sixty are listed, to keep the page short.
• Prime limit. Limits above one hundred thousand are capped so the browser stays responsive.
• Definition of prime. One is neither prime nor composite, and the tool reports it as not prime accordingly.