basic

Number of Divisors from Prime Factorisation Calculator

d(n) = (e₁+1)(e₂+1)… — count of all divisors.

Calculates the number of positive divisors of n = p₁^e₁ × p₂^e₂ × … as d(n) = (e₁+1)(e₂+1)…. For small n, also computes the sum of divisors σ(n) = Π(p^(e+1)−1)/(p−1).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

d(n) = Π(eᵢ+1); σ(n) = Π[(pᵢ^(eᵢ+1)−1)/(pᵢ−1)]

In depth

Calculates the number of positive divisors of n = p₁^e₁ × p₂^e₂ × … as d(n) = (e₁+1)(e₂+1)…. For small n, also computes the sum of divisors σ(n) = Π(p^(e+1)−1)/(p−1).