Math & Education
Prime Number Checker / Factorizer
Check if a number is prime, view its divisors, prime factorization, and nearest prime numbers.
Inputs
Results
Primality Result
Yes (Prime)
Prime Factorization
-
Divisors
-
Nearby Primes
-
How It Works
A prime number is an integer greater than 1 that has no positive divisors other than 1 and itself. The checker uses trial division by factoring primes ($2, 3$, and $6k \pm 1$ sequences) up to the square root of the number to confirm primality in $\mathcal{O}(\sqrt{N})$ complexity.\n\nPrime factorization breaks the number into its component prime multipliers using prime factor division, and divisors are aggregated by factoring the modular products.
Formula Used
Primality Test: Check if N mod i = 0 for i from 2 up to √N
A composite number must have a prime factor less than or equal to its square root. If no integers in this range divide N evenly, then N has no factors other than 1 and itself, making it prime.
Worked Example
Here is a step-by-step example of how these values are calculated:
Number
97
Result: Result: Prime Number. Divisors: 1, 97. Adjacent: Prev: 89, Next: 101.
Frequently Asked Questions
Why is 1 not considered a prime number?
By mathematical definition, prime numbers must have exactly two distinct positive divisors: 1 and themselves. Since 1 has only one divisor (itself), it is classified as neither prime nor composite.
What is the largest prime checked?
To ensure browser page responsiveness and prevent tab freezes from heavy computational loops, this offline tool caps checking input values at 1,000,000.