Prime factorization: break n into primes, e.g., 360 = 23 × 32 × 5.
Divisors: all positive integers that divide n with no remainder.
τ(n) (divisor count): Π (ei+1) over prime exponents ei.
σ(n) (sum of divisors): Π ( (pei+1 − 1)/(p − 1) ). Proper-divisor sum = σ(n) − n.
Perfect: proper-divisor sum = n. Abundant: > n. Deficient: < n.
Prime vs. Composite: τ(n)=2 ⇒ prime; otherwise composite. n=1 is a “unit”.
Tip: Use underscores/commas for readability (e.g., 2_147_483_647). They’re ignored.
Performance notes
Uses optimized trial division (fast for typical calculator inputs up to ~1012–14).
For extremely large integers, factorization can be slow—try a smaller number.
Cookies & privacy
Utilities Bunker uses necessary cookies to run the site. Optional cookies help remember preferences,
measure usage, and improve the platform. You can change your choices any time.
Privacy Policy.
