Prime Checker

Prime Number Checker

Check whether a number is prime, see its full prime factorisation, all divisors, and the nearest primes above and below.

 
Prime factorisation
Number of divisors
Sum of divisors
Previous prime
Next prime

All divisors

Works on whole numbers up to 9,007,199,254,740,991 — the largest integer JavaScript can hold exactly. Beyond that the arithmetic itself stops being reliable, so the tool declines rather than guessing.

Last updated 28 August 2026

What the factorisation tells you

Every whole number above one is either prime or a unique product of primes, and that product is more informative than it first looks. The number of divisors falls straight out of it: add one to each exponent and multiply. So 360, which factors as 2³ × 3² × 5, has 4 × 3 × 2 = 24 divisors without anyone needing to list them. Primality testing here uses trial division up to the square root, which is enough for any number this tool accepts — if nothing below the square root divides it, nothing above will either, because factors come in pairs that straddle that point.

Common questions

Why only check divisors up to the square root?

Because factors come in pairs. If a number has a factor larger than its square root, the matching factor must be smaller than the square root — so if nothing small divides it, nothing large will either. That cuts the work enormously.

Is 1 a prime number?

No. A prime has exactly two distinct divisors, one and itself. The number 1 has only one divisor, so it fits neither the definition of prime nor composite — it sits on its own.

How large a number can it handle?

Up to 9,007,199,254,740,991, which is the largest integer JavaScript can represent exactly. Above that, ordinary arithmetic starts losing precision, so the tool declines the input rather than returning a confident wrong answer.

What does the sum of divisors mean?

It adds up every divisor including the number itself. It is how perfect numbers are defined — a number whose divisors excluding itself add up to the number, like 6 (1 + 2 + 3) or 28.

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