Prime Number Calculator
Check if a number is prime, find all prime factors, and list primes up to any number.
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Prime factors
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What is Prime Number Calculator?
A prime number calculator checks whether a number is prime, finds the prime factorization of any integer, and lists all prime numbers up to a given limit. Prime numbers are integers greater than 1 that have no divisors other than 1 and themselves, and they are the building blocks of all integers.
How to use
- 1 Enter a number in the 'Check if a number is prime' field to instantly see if it's prime.
- 2 Enter a number in the 'Prime factorisation' field to see it broken down into its prime factors.
- 3 Enter a number (up to 1000) in the 'List primes up to N' field to see all primes in that range.
- 4 All three sections work independently — use whichever you need.
Formula
Example calculation
97 is prime because no integer from 2 to √97 ≈ 9.8 divides it evenly. The prime factorization of 360 is 2³ × 3² × 5 (i.e., 2 × 2 × 2 × 3 × 3 × 5 = 360).
Frequently asked questions
Is 1 a prime number?
No. By definition, prime numbers must be greater than 1. The number 1 is neither prime nor composite — it's a unit.
What is the smallest prime number?
2 is the smallest prime number and the only even prime. All other even numbers are divisible by 2 and therefore not prime.
How do you find prime factors?
Use trial division: start with 2 and divide the number repeatedly while it's divisible. Move to the next integer and repeat until the remaining value is 1.
What is a prime factorization used for?
Prime factorization is used to find the GCF and LCM of numbers, simplify fractions, and solve problems in cryptography (RSA encryption relies on the difficulty of factoring large primes).
Are there infinitely many primes?
Yes. Euclid proved over 2000 years ago that there are infinitely many prime numbers. The proof shows that any finite list of primes can always be extended.