Prime Number Calculator — Test Primality & Factorize

Reviewed

Enter details
ResultUpdates as you type
Is Prime?Yes — It is a Prime Number
Next Prime31
Previous Prime23
Factor Count1

Check if a number is prime, find prime factors, next prime, and previous prime instantly with complete step-by-step factorization.

Test whether any integer is a prime number and discover its prime factors, next prime, and previous prime.

Understanding Prime Numbers

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Numbers greater than 1 that are not prime are called composite numbers.

Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either a prime number itself or can be uniquely represented as a product of prime numbers (up to the order of factors).

How to use

  1. Enter any positive integer (N).
  2. The tool tests for primality.
  3. View whether it is prime, its prime factors, next prime, and previous prime.

Formula

Prime Definitionn > 1 with no positive divisors other than 1 and nA natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
Prime Factorizationn = p1^a1 × p2^a2 × ... × pk^akDecomposition into a product of prime numbers.

Worked examples

Checking Primality

For N = 29: 29 is prime because its only divisors are 1 and 29. Next prime is 31, previous prime is 23.

Frequently asked questions

Is 1 a prime number?

No, by definition 1 is neither prime nor composite.

What is the smallest prime number?

The number 2 is the smallest prime number and the only even prime number.

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