Prime Number Checker
Check whether a number is prime, and see its full prime factorization if it isn't.
What makes a number prime
A prime number is a whole number greater than 1 that has exactly two positive divisors: 1 and itself. Numbers with more than two divisors are called composite. By this definition, 1 is neither prime nor composite, and 2 is the only even prime number — every other even number is divisible by 2, disqualifying it.
This calculator checks primality by testing whether any number up to the square root of your input divides it evenly — if none do, the number is prime. This is an efficient method since any factor larger than the square root would need a corresponding factor smaller than it.
Prime factorization explained
Every composite number can be broken down into a unique set of prime factors — for example, 84 = 2 × 2 × 3 × 7. This is known as the Fundamental Theorem of Arithmetic, and it's the basis for many areas of number theory and cryptography.
Prime factorization has practical applications beyond pure math — it's foundational to encryption algorithms like RSA, which rely on the fact that factoring very large numbers into their prime components is computationally difficult.
Frequently asked questions
Is 1 a prime number?
No — by definition, a prime number must have exactly two distinct positive divisors (1 and itself). Since 1 only has one divisor (itself), it's excluded from being prime.
Why is 2 the only even prime number?
Every even number greater than 2 is divisible by 2 in addition to 1 and itself, giving it at least three divisors — which disqualifies it from being prime by definition.