Prime Number Checker & Prime Factorization

Check if a number is prime, find its prime factors and divisors, and the nearest primes — for numbers up to 24 digits.

Last updated:

360—
Prime factors
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Number of divisors
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Previous prime
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Next prime
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Is it a prime number?

This prime number checker tells you instantly whether a number is prime and, if it isn't, breaks it into its prime factors — the standard way to find HCF and LCM, simplify fractions and square roots. It also lists all divisors for smaller numbers and finds the nearest primes on either side. Large numbers up to 24 digits are tested with a proven fast method.

How to use it

  1. Type any whole number.
  2. See whether it's prime, its factorisation and its divisors.

Primes below 100

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

Example

360 is composite: 360 = 2³ × 3² × 5, so it has (3+1)(2+1)(1+1) =24 divisors — one reason 360 degrees make such a convenient circle. 97 is the largest prime below 100, and 1,000,000,007 is a famous prime used in programming contests. Find HCF and LCM with the LCM & HCF calculator.

Frequently asked questions

What is a prime number?
A whole number greater than 1 whose only factors are 1 and itself: 2, 3, 5, 7, 11, 13… A number with more factors, like 12 (= 2 × 2 × 3), is called composite. 1 is neither prime nor composite.
How does the checker test large numbers?
Small numbers are tested by trial division. Large numbers (up to 24 digits) use the Miller–Rabin test with a fixed set of bases that is proven to give the correct answer in that range.
What is prime factorisation?
Writing a number as a product of primes, such as 360 = 2³ × 3² × 5. Every whole number above 1 has exactly one prime factorisation, which is why primes are called the building blocks of numbers.
Is 2 the only even prime?
Yes. Every other even number is divisible by 2, so it has at least three factors (1, 2 and itself).

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