Prime Number Checker
Check whether a number is prime, and if not, get its full prime factorisation. Handles large numbers fast, with the divisibility working shown. Free, in your browser.
Prime Number Checker and Factoriser
How to Use the Prime Checker
Enter a number
Type any whole number — small or large, up to fifteen digits.
See if it is prime
The checker tells you instantly whether the number is prime (divisible only by 1 and itself) or composite.
Get the factorisation
If the number is composite, you get its full prime factorisation — the unique set of primes that multiply to make it, with exponents.
Understand the result
A short note explains the verdict — how many divisors the number has, or how far the primality check looked. Need the GCD or LCM next? That tool is one click away.
Primes and Factorisation
The Atoms of Arithmetic
A prime number is a whole number greater than 1 whose only divisors are 1 and itself — 2, 3, 5, 7, 11, 13, and so on. Every other whole number bigger than 1 is "composite", meaning it can be broken down into a product of primes. This is not just a definition; it is one of the deepest facts in mathematics, the Fundamental Theorem of Arithmetic: every whole number has exactly one prime factorisation, up to the order of the factors. Primes are, in that sense, the atoms of arithmetic — the indivisible building blocks from which every other number is assembled. 1001, for instance, looks unremarkable but factors cleanly into 7 × 11 × 13, three consecutive primes. This tool answers the two questions people actually ask: is my number prime, and if not, what are its prime factors? It checks primality by testing divisibility only up to the square root of the number — because if a number has a factor larger than its square root, it must also have one smaller, so there is no need to look further — which is why it can settle even large numbers almost instantly.
Prime factorisation is the engine behind a surprising amount of everyday maths. It is how fractions are simplified (you cancel the common prime factors), how the GCD and LCM are computed, and how you reason about divisibility. It is also the foundation of modern cryptography: the security of RSA encryption rests on the fact that multiplying two large primes is easy, but factoring their product back into those primes is, for big enough numbers, practically impossible — a beautiful asymmetry that protects much of the internet. The numbers this tool factors are far smaller than cryptographic primes, but the same idea is at work, and seeing a number resolve into its prime parts builds the intuition that makes the cryptographic version make sense.
"Primes are the atoms of number. Every whole number is built from them in exactly one way — and that uniqueness is what makes factorisation so powerful."
From Curiosity to Cryptography
People reach for a prime checker for all sorts of reasons. Students meet primes and factorisation early and search constantly to check homework or settle "is 1,001 prime?" arguments. Programmers and number-theory hobbyists use it while exploring problems — hashing, modular arithmetic, project-Euler-style puzzles. And the simply curious like to test birthdays, years, and oddly satisfying numbers. Whatever the reason, the value is the same: an instant, correct answer, plus the factorisation that explains it, with no fuss and no sign-up. Because the check runs entirely in your browser using an efficient algorithm, even fairly large numbers resolve in a blink, and nothing you type ever leaves your device. It is a small window onto one of the richest and most consequential ideas in all of mathematics.
10 Facts About Prime Numbers
A prime is a whole number above 1 divisible only by 1 and itself.
2 is the only even prime — every other even number is divisible by 2.
Every whole number above 1 has exactly one prime factorisation.
To test primality you only need to check divisors up to the square root.
1,001 = 7 × 11 × 13 — three consecutive primes.
There are infinitely many primes — proved by Euclid around 300 BC.
The number 1 is neither prime nor composite — it is a "unit".
The security of RSA encryption rests on how hard factoring large numbers is.
The largest known prime has over 41 million digits (a Mersenne prime).
Primes are the building blocks behind GCD, LCM, and fraction simplification.
Frequently Asked Questions
- A number is prime if its only divisors are 1 and itself. This tool checks that for you instantly by testing divisibility against the primes up to the number's square root — if none divide it, it is prime. If one does, the number is composite and you get its full factorisation.
- No. By definition a prime is a whole number greater than 1, so 1 is neither prime nor composite — it is called a "unit". The tool flags this explicitly if you enter 1 (or 0), rather than giving a misleading yes/no.
- It is breaking a composite number into the unique product of primes that makes it — for example 360 = 2³ × 3² × 5. Every whole number above 1 has exactly one such factorisation. The tool shows it in exponent form and, where useful, fully expanded.
- Because divisors come in pairs that multiply to the number: if a number has a factor larger than its square root, the matching factor must be smaller than the square root. So if nothing up to the square root divides it, nothing above will either. This makes the check very fast, even for large numbers.
- Up to about fifteen digits, which covers everything from classroom numbers to large curiosities. The primality test and factorisation use efficient trial division up to the square root, so results come back almost instantly within that range.
- Yes. Every even number is divisible by 2, so any even number bigger than 2 has 2 as a factor and cannot be prime. That makes 2 the unique even prime — every other prime is odd.
- Primes underpin simplifying fractions, computing GCD and LCM, and reasoning about divisibility. On a larger scale, the difficulty of factoring the product of two big primes is the basis of RSA encryption, which secures much of the internet. The same idea, scaled down, is what you see here.
- Primality is defined for positive integers, so the tool considers the absolute value when factorising. Conventionally, primes are positive; negatives are handled by factoring their magnitude.
- Yes. The check runs entirely in your browser — nothing is uploaded, stored, or logged — and it works offline once loaded. It is private and instant.
- Completely free, with no account, sign-up, or limit. It runs entirely in your browser and collects no data. Use it as often as you like.
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