2310

2310 is a natural number that comes after 2309 and before 2311. In mathematics it is notable for its prime factorization and its role as a primorial.

The prime factorization of 2310 is 2 × 3 × 5 × 7 × 11, meaning it is squarefree and the product of the first five primes. This makes 2310 the 11th primorial, often denoted 11#. Its divisors are all possible products of any subset of the prime factors, yielding 2^5 = 32 positive divisors, including 1 and 2310 itself.

Arithmetic characteristics follow from its factorization. Euler’s totient function gives φ(2310) = 480, representing the number of integers between 1 and 2310 that are relatively prime to 2310. The sum of divisors is σ(2310) = 6912, since for a squarefree n with primes p1, p2, ..., pk, σ(n) = ∏(1 + pi). The divisor count and the squarefree nature also imply that 2310 has many divisors but no repeated prime factors.

In broader context, 2310 is often cited as an example of a highly factorable, squarefree number and serves as a concrete instance of a primorial. It highlights how the product of initial primes yields a number with a relatively large divisor set and specific arithmetic function values, useful in number theory demonstrations and computations.