Número de Divisores τ(n)

This calculator determines the number of positive divisors of a positive integer n, denoted by τ(n) (tau of n). The function τ(n) counts exactly how many positive integers divide n without leaving a remainder. For example, τ(12) = 6, because the divisors of 12 are 1, 2, 3, 4, 6, and 12. The calculation is based on the prime factorization of n: if n = p₁^a₁ × p₂^a₂ × ... × p_k^a_k, then τ(n) = (a₁+1)(a₂+1)...(a_k+1).

To use the calculator, simply enter a positive integer in the input field and click 'Calculate'. The result will display the value of τ(n) and, in many cases, also the list of divisors. This tool is useful for mathematics students, teachers, and enthusiasts who need to explore number properties, such as classifying numbers as primes (τ=2), perfect squares (odd τ), or highly composite numbers.

Use cases include checking if a number is prime (τ=2), discovering if a number is a perfect square (odd τ), or comparing the number of divisors between two numbers. Caveats: the calculator only accepts positive integers; negative or decimal values will produce an error. Additionally, very large numbers may require extra processing, but the tool handles reasonable values.