Prime Number Checker
Type any whole number up to a trillion. You get a yes-or-no answer, the prime factorization, every divisor and the reasoning behind it — no signup, nothing sent anywhere.
Primes from 1 to 100
The 25 highlighted numbers are prime. Tap any square to run it through the checker.
What makes a number prime
A prime number is a whole number above 1 with exactly two divisors: 1 and itself. Everything else above 1 is composite — it can be built by multiplying smaller numbers. That single rule turns out to be the backbone of arithmetic: every whole number above 1 factors into primes in exactly one way, which is why primes are called the atoms of the number system.
How to test a number by hand
- Stop at the square root. To test 97, you only need divisors up to √97 ≈ 9.8. Anything bigger would have to pair with something smaller you already checked.
- Rule out the easy ones. Even numbers (except 2) fail immediately. If the digits add to a multiple of 3, it is divisible by 3. If it ends in 0 or 5, it is divisible by 5.
- Test the primes that are left. For 97 that means 7 only — and 97 ÷ 7 leaves a remainder, so 97 is prime.
This checker does exactly that, just faster: it walks the candidates 2, 3, then every number of the form 6k ± 1 up to the square root, because every prime above 3 has that shape.
Why prime factorization is worth knowing
Once a number is broken into primes, several school problems become mechanical. Simplifying a fraction is cancelling shared primes. The greatest common divisor is the primes two numbers share, and the least common multiple is every prime at its highest power. Even the count of divisors falls out of the exponents: 360 = 2³ × 3² × 5 has (3+1) × (2+1) × (1+1) = 24 divisors, without listing one of them.
Frequently asked questions
What is a prime number?
A whole number above 1 whose only divisors are 1 and itself. 7 is prime; 9 is not, because 3 divides it.
Is 1 a prime number?
No. A prime needs exactly two distinct divisors and 1 has only one. Excluding it is also what makes prime factorization unique.
Is 2 prime?
Yes — and it is the only even prime. Every other even number has 2 as a third divisor.
How many primes are there under 100?
25: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. The chart above highlights them.
Do primes ever run out?
No. Euclid's proof: multiply any finite list of primes and add 1 — the result has a prime divisor missing from your list, so no list is ever complete.
How big a number can this handle?
Up to 1,000,000,000,000 (10¹²). Beyond that, honest trial division gets too slow to run comfortably in a browser.
More tools: fraction calculator · long division · rounding practice · times tables · printable worksheets · today's puzzle.