Prime Number Calculator: Check If a Number Is Prime

A prime number is a whole number greater than 1 that has exactly two divisors: 1 and itself. To check a number, try dividing it by every whole number up to its square root. If none divides it evenly, it is prime.

This check pairs well with the LCM and GCD calculator, which uses the same idea of divisors to compare two numbers.

Prime numbers also appear in counting problems, so if you want to count arrangements, try the permutation and combination calculator.

To factor a number, divide it by the smallest prime that divides it evenly, then repeat with the quotient until only 1 remains. The divisors you used, with their counts, are the prime factorization.

For example, 60 divided by 2 gives 30, divided by 2 gives 15, divided by 3 gives 5, and divided by 5 gives 1. So 60 = 2^2 x 3 x 5.

Check 29: its square root is about 5.39, so test the primes 2, 3 and 5. None divides 29 evenly, so 29 is prime, and its only prime factor is 29 itself.

Check 60: it is even, so 2 divides it, and it is not prime. Its factorization is 60 = 2^2 x 3 x 5.

The primes up to 20 are 2, 3, 5, 7, 11, 13, 17 and 19. There are 8 of them.

The table below lists every prime up to 50. Use it to check small numbers quickly, or enter a number above to test any whole number and see its factors.

1 is not a prime number: it has only one divisor, itself, while a prime needs exactly two. 2 is the only even prime, because every other even number is divisible by 2.

A number with a factor other than 1 and itself is composite, not prime. Checking divisors only up to the square root is enough, because any larger factor pairs with a smaller one you would already have found.