Prime Number Checker & Factorisation
Check whether a number is prime and find its factors.
Tip: A prime number is divisible only by 1 and itself (e.g. 2, 3, 5, 7, 11…).
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About this digital tool
This tool checks whether a number is prime and breaks it into prime factors. In "Check" mode you enter a number and get the answer, the factorisation, as well as the previous and next prime. In "List" mode all prime numbers up to a limit are shown, at most 1000.
A prime number is one that is divisible only by 1 and itself. To test it, it is enough to check divisors up to its square root: 97 is not divisible by 2, 3, 5 or 7, so it is prime. The factorisation of 84 is 2 × 2 × 3 × 7, that is 2² × 3 × 7. Factorisation is used for simplifying fractions, for GCD and LCM and in cryptography.
How to use
- Choose "Check" mode for a single number or "List" for a range of numbers.
- In "Check" enter the number; in "List" enter the upper limit (up to 1000).
- Read the answer: prime or not, together with the prime factorisation.
- See the previous and next prime, or the list of numbers found.
Frequently asked questions
Is 1 a prime number?
No — by the mathematical definition, 1 is neither prime nor composite. The first prime number is 2.
How do I know if a number is prime?
Try dividing it by the primes up to its square root. If none divides it without a remainder, the number is prime. E.g. √97 ≈ 9.8 and 97 is not divisible by 2, 3, 5, 7.
Which are the prime numbers up to 20?
2, 3, 5, 7, 11, 13, 17 and 19. That is eight numbers in all, and 2 is the only even prime.
What is prime factorisation?
It is writing a number as a product of primes. E.g. 84 = 2 × 2 × 3 × 7. Every whole number greater than 1 has exactly one factorisation.