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Prime Factorisation Calculator

Work out prime factorisation instantly with clear inputs, formula shown and shareable results.

About Prime Factorisation Calculator

The fundamental theorem of arithmetic guarantees every integer above 1 has a unique prime factorisation. Once written as p₁^e₁ × p₂^e₂ × …, the divisor count is the product of (eₖ + 1).

Formula

Divisor count

d(n) = Π (eₖ + 1) over the prime exponents

Worked example

With the default values below, Prime Factorisation Calculator returns Prime factorisation of 2^4 × 3^2 × 5 × 7. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number to factoriseminimum 2
5,040
Also count the divisorsone of Yes, No
Yes

Results

Prime factorisation
2^4 × 3^2 × 5 × 7
Distinct prime factors
4
Total divisors
60
Largest prime factor
7

Step by step

  1. 1Values used
  2. 2Divisor count
  3. 3Prime factorisation= 2^4 × 3^2 × 5 × 7
  4. 4Distinct prime factors= 4
  5. 5Total divisors= 60
  6. 6Largest prime factor= 7

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Factorise 5040.

2⁴ × 3² × 5 × 7, which has 5 × 3 × 2 × 2 = 60 divisors.

Why is the factorisation unique?

Euclid's lemma forces any prime dividing a product to divide one of the factors, which pins the decomposition down exactly.

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