Prime Number Checker
Enter any whole number to instantly check whether it's a prime number — and if it isn't, see its complete list of factors.
How the Prime Number Checker formula works
A number is prime if it has no divisors other than 1 and itself:
For n, check every integer from 2 up to √n If any of them divide n evenly, n is not prime
Only checking up to the square root is a well-known optimization: if n has a factor larger than √n, it must also have a corresponding factor smaller than √n, so any factor pair would already have been found.
Step-by-step calculation
- Rule out numbers less than 2, which aren't prime by definition.
- Test divisibility by every integer from 2 up to the square root of the number.
- If none divide evenly, the number is prime. If any does, the number is composite, and all its factors are listed.
Worked example
Checking 97: testing divisors 2 through 9 (since √97 ≈ 9.85), none divide evenly — 97 is prime. Checking 96: 2 divides evenly, so 96 is not prime, with factors 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
Frequently asked questions
Is 1 a prime number?
No — by definition, a prime number has exactly two distinct positive divisors (1 and itself). Since 1 only has one divisor, it's classified as neither prime nor composite.
Is 2 the only even prime number?
Yes — every other even number is divisible by 2 in addition to 1 and itself, which means it has at least three divisors and can't be prime.