How factoring works
Integer factoring: trial-divide by primes 2, 3, 5, 7, 11, … up to √n. Each prime that divides cleanly is recorded with its multiplicity. The full divisor list is built from every combination of those primes.
Quadratic factoring: the roots r₁, r₂ from the quadratic formula give the factored form a(x − r₁)(x − r₂). When the roots are rational, this is rewritten with integer coefficients as (px + q)(rx + s).
FAQ
What if my quadratic has no real roots?
Then b² − 4ac < 0 and the polynomial cannot be factored over the real numbers. The calculator reports "irreducible over ℝ" and lists the complex roots.
How big a number can I factor?
The integer factoriser uses trial division and is efficient for numbers up to about 10¹². Beyond that runtime grows quickly; use the big number calculator for larger values.
Is 1 prime?
By convention, no. 1 has only one divisor (itself), and we exclude it from the prime list to keep the fundamental theorem of arithmetic clean (each n > 1 has a unique prime factorisation).