Prime Number Calculator
Check if a number is prime, find all prime factors, and list primes up to any number.
How to use this calculator
👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉
In plain English — what does this do?
🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.
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.
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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 it
- 1️⃣ Enter a number in the 'Check if a number is prime' field to instantly see if it's prime.
- 2️⃣ Enter a number in the 'Prime factorisation' field to see it broken down into its prime factors.
- 3️⃣ Enter a number (up to 1000) in the 'List primes up to N' field to see all primes in that range.
- 4️⃣ All three sections work independently — use whichever you need.
Formula
💡 See it in action — a real example
❓ Common 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.