Number Theory
Advanced

Number of Divisors

Count of divisors from prime factorization exponents.

Formula

d(n)=∏(ai+1)d(n) = \prod (a_i + 1)

Variables

a_iPrime exponents

Example

12=2²·3: (2+1)(1+1)=6

Did You Know?

The number of divisors comes straight from the prime factorisation, a neat trick of exponents plus one.

divisorsfactorization