Prime Number Checker
Type a number, find out whether anything divides into it.
Prime Number Checker
What Makes a Number Prime
A prime has exactly two distinct divisors: itself and one. That wording matters, because it is what rules out the number 1, which has only a single divisor and therefore fails the test. 2 qualifies and is the only even number that ever will, since every other even number is divisible by 2.
You Only Need to Check to the Square Root
To test 97 you do not divide by every number below it. Factors come in pairs that multiply to the original, and one of each pair is always at or below the square root. Since the square root of 97 is a little under 10, checking 2, 3, 5 and 7 settles it. Nothing divides in, so 97 is prime.
That shortcut is why testing a six-digit number is still instant rather than a thousand divisions.
Why Anyone Cares
Primes are the building blocks of every other whole number: any integer above 1 is either prime or a unique product of primes. That uniqueness is what makes prime factorisation useful for finding common denominators, simplifying fractions, and the key exchange behind most encrypted connections.
Reading the Factor List
When a number is not prime this page lists what divides it. 91 looks prime to most people until you see 7 times 13. Seeing the factor pair is usually more useful than the yes or no answer on its own.