Prime Number Checker & Factoriser
Checks whether a number is prime and shows its complete prime factorisation.
Last updated
How to check if a number is prime
- Type a whole number.
- See straight away whether it’s prime and, if not, its prime factorisation, for example 360 = 2³ × 3² × 5.
How this works
A number is prime if it has exactly two divisors: 1 and itself. This checks divisibility up to the square root of the number for efficiency, then finds the full prime factorisation by repeated division.
Very large numbers (above roughly 10 trillion) may take a moment or be impractical to factorise in-browser.
Questions about prime numbers
What is a prime number?
A whole number greater than 1 that can only be divided exactly by 1 and itself. The first primes are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
Is 1 a prime number?
No. A prime must have exactly two different divisors, and 1 has only one. 2 is the smallest prime, and the only even one.
What is prime factorisation?
Writing a number as primes multiplied together. 84 = 2 × 2 × 3 × 7, or 2² × 3 × 7. Every whole number above 1 has exactly one prime factorisation.
How big a number can it check?
Numbers up to around 10 trillion are checked quickly. Much larger numbers can take a long time to factorise in a browser.