Work out prime factorisation instantly with clear inputs, formula shown and shareable results.
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).
Divisor count
d(n) = Π (eₖ + 1) over the prime exponents
2⁴ × 3² × 5 × 7, which has 5 × 3 × 2 × 2 = 60 divisors.
Euclid's lemma forces any prime dividing a product to divide one of the factors, which pins the decomposition down exactly.