Divisor Count of 720

Example of Use of $\tau$ Function

 * $\tau \left({720}\right) = 24$

where $\tau$ denotes the $\tau$ Function.

Proof
From Tau Function from Prime Decomposition:
 * $\displaystyle \tau \left({n}\right) = \prod_{j \mathop = 1}^r \left({k_j + 1}\right)$

where:
 * $r$ denotes the number of distinct prime factors in the prime decomposition of $n$
 * $k_j$ denotes the multiplicity of the $j$th prime in the prime decomposition of $n$.

We have that:
 * $720 = 2^4 \times 3^2 \times 5$

Thus:

The divisors of $720$ can be enumerated as:
 * $1$, $2$, $3$, $4$, $5$, $6$, $8$, $9$, $10$, $12$, $15$, $16$, $18$, $20$, $24$, $30$, $36$, $40$, $45$, $48$, $60$, $72$, $80$, $90$, $120$, $144$, $180$, $240$, $360$, $720$