Divisors, τ(n) & σ(n)

Divisor list, count, and sum of divisors

About this calculator

The Divisor Function Calculator lists every divisor of a positive integer and computes τ(n), the number of divisors, and σ(n), the sum of divisors. It pairs complementary divisors (a × b = n), highlights perfect squares, and classifies n as perfect, abundant, or deficient. Useful for number theory, divisibility, and exploring perfect numbers.

How to use the Divisors, τ(n) & σ(n) calculator

  1. Enter the values for your problem into the input fields.
  2. Read the result — it updates instantly as you type.
  3. Check the formula and the visual explanation to follow how the answer was found.
  4. Copy the page URL to share the exact calculation.

Common examples

  • 12 → divisors 1, 2, 3, 4, 6, 12 · τ(12) = 6 · σ(12) = 28 · abundant
  • 28 → divisors 1, 2, 4, 7, 14, 28 · σ(28) = 56 = 2 × 28 · perfect
  • 13 (prime) → divisors 1, 13 · τ(13) = 2 · σ(13) = 14 · deficient
  • 36 (perfect square) → 9 divisors, τ(36) is odd, √36 = 6 pairs with itself
  • 1 → only divisor is 1 · τ(1) = 1 · σ(1) = 1 · deficient

Frequently asked questions

How does the Divisors, τ(n) & σ(n) calculator work?

Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.

When would I use the Divisors, τ(n) & σ(n) calculator?

It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.

How accurate are the results?

Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.