Math calculators
Primes, factors, GCD and LCM
Free prime number checker and factorisation calculator, with divisors, next and previous prime, and GCD and LCM of a list of integers.
Inputs
Results
Methodology
Conventions
- Primality uses a deterministic Miller–Rabin test, exact for every n in range (1 to 10¹⁵).
- Factorisation is by trial division by 2, 3 and numbers of the form 6k ± 1.
References
- Crandall and Pomerance, Prime Numbers: A Computational Perspective (2005)
Formulas
- Factorisation
- n = \prod p_i^{e_i}
- Number of divisors
- d(n) = \prod (e_i + 1)
- Sum of divisors
- \sigma(n) = \prod \frac{p_i^{e_i + 1} - 1}{p_i - 1}
- LCM
- \operatorname{lcm}(a, b) = \frac{|ab|}{\gcd(a, b)}