Prime Number Checker
Check whether any number is prime and find its smallest factor.
Enter any whole number to find out instantly whether it's prime, and if not, see its smallest factor and factorization. Great for homework, cryptography curiosity, and settling debates about numbers like 91 (it's 7 × 13).
How it's calculated
The checker tests divisibility by every integer up to the square root of the number (trial division). If none divide it evenly, the number is prime; otherwise the first divisor found is its smallest factor.
Frequently asked questions
Is 1 a prime number?
No. A prime number must have exactly two divisors (1 and itself), and 1 has only one divisor, so it is neither prime nor composite.
Why does it only check divisors up to the square root?
If a number has a factor larger than its square root, it must also have a matching factor smaller than the square root — so checking up to √n catches every factor pair.
Is 91 prime?
No — 91 = 7 × 13. It's a classic trick question because 91 looks prime at first glance.