Factor Calculator

List every factor of a positive integer, plus its prime factorization.

Equation used
Trial division up to sqrt(n) finds all factors; repeated division by primes gives n = p_1^e_1 × p_2^e_2 × ·s

Frequently Asked Questions

How does it find every factor so quickly?

It only needs to test divisors up to √n — for each divisor i that divides n evenly, both i and n/i are factors, so it finds matching pairs without checking every number up to n.

What does "factor pairs" mean?

Each pair is two factors that multiply together to give the original number (e.g. for 12: 1×12, 2×6, 3×4). Every factor in the full list belongs to exactly one such pair.

Why is there a limit of 100,000,000?

The trial-division method checks divisors up to √n in the browser, so it's capped at numbers up to 100 million to keep the calculation fast and responsive.