You enter a positive integer. The tool uses trial division — testing every integer from 1 up to the square root of the number — to find all factors. For each divisor that divides evenly, it records both the divisor and its complement. Prime factorization is computed by repeatedly dividing by the smallest prime factor until the quotient reaches 1. The primality test uses the same trial division approach with a 6k±1 optimization.
If a number n has a factor larger than √n, the corresponding paired factor must be smaller than √n. So by testing up to √n, you are guaranteed to find every factor pair without redundant checks.
No. By modern convention, 1 is neither prime nor composite. Primes are defined as integers greater than 1 with exactly two distinct positive divisors (1 and themselves). Excluding 1 keeps the Fundamental Theorem of Arithmetic (unique prime factorization) clean.
JavaScript uses 64-bit floating-point numbers, which can exactly represent integers up to 2⁵³ (about 9 quadrillion). For very large numbers in the billions, the trial division may take a noticeable moment to complete since it checks up to √n divisors.
Prime factorizations are essential in cryptography (RSA encryption relies on the difficulty of factoring large semiprimes), simplifying fractions (find the GCF), computing LCMs for scheduling problems, and number theory research.
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.