Prime Number Checker
Check if a number is prime, find all prime factors, and list all primes within a range. Instant results with factorization breakdown.
Is this number prime?
What Are Prime Numbers?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13…
Prime factorization expresses any composite number as a product of primes. Example: 360 = 2³ × 3² × 5.
2 is the only even prime number. All other primes are odd.
1 is not considered prime by convention — it has only one divisor (itself).
Frequently Asked Questions
A prime number is greater than 1 and has exactly two distinct divisors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
No. By mathematical convention, 1 is not considered prime because prime numbers are defined as having exactly two distinct divisors, and 1 only has one divisor (itself).
Prime factorization breaks a number into a product of prime numbers. Every integer greater than 1 has a unique prime factorization. Example: 60 = 2² × 3 × 5.
To check if n is prime, test divisibility by all integers up to √n. If none divide evenly, the number is prime. This calculator uses that method.
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