Divisors, τ(n) & σ(n)

Divisor list, count, and sum of divisors

12 → τ(n) = 6 · σ(n) = 28
Number of divisors τ(n)
6
Sum of divisors σ(n)
28
Sum of proper divisors s(n)
16
Classification
Abundant (σ(n) > 2n)
Divisors of n (6)
1234612
Divisor pairs (a × b = n)
1 × 122 × 63 × 4
Divisors of n placed on a line with arcs linking each complementary pair a and b where a × b = n, and a panel summarizing τ(n), σ(n) and the perfect/abundant/deficient classification.Divisors of n placed on a line with arcs linking each complementary pair a and b where a × b = n, and a panel summarizing τ(n), σ(n) and the perfect/abundant/deficient classification.τ(12) = 6σ(12) = 28Abundant1234612

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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.

Häufige Beispiele

  • 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