Prime Number Checker

How to use the prime number checker

1. Fill in the fields — they start with a worked example.
2. Read the answer, and the arithmetic shown beneath it.
3. Copy the results, or adjust the inputs to compare scenarios.

About this tool

A prime has exactly two divisors: one and itself. Everything else breaks down into primes in exactly one way — the fundamental theorem of arithmetic — which is what the factorisation shows.

Trial division only needs to reach the square root of the number, because any larger factor must pair with a smaller one already tested. That is why checking even large numbers is quick.

Common uses

• Checking whether a number is prime.
• Finding the prime factors for schoolwork.
• Listing all divisors of a number.

Frequently asked questions

Is 1 a prime number?

No. A prime has exactly two distinct divisors, and 1 has only one. Excluding it keeps prime factorisation unique.

Why only check up to the square root?

Because factors come in pairs. If a number has a factor above its square root, the matching factor is below it and has already been found.