Trial division repeatedly removes the smallest available prime factor. Once the candidate squared exceeds the remaining value, that remainder is either one or a final prime factor.
Skip impossible candidates
After 2 and 3, every prime greater than 3 is adjacent to a multiple of 6, so checking 6k−1 and 6k+1 avoids obvious composites without changing the answer.
Reproduce important arithmetic
PrimeFactor performs exact integer recomposition and primality checks before displaying a result. For important downstream use, repeat the multiplication independently and apply only the rules of the neutral integer problem you intend to solve. The tool does not assess cryptographic strength or approve any safety-critical design.