Divisor Count of 17,796,126,877,482,329,126,044

Example of Use of $\tau$ Function

 * $\tau \left({17 \, 796 \, 126 \, 877 \, 482 \, 329 \, 126 \, 044}\right) = 48$

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:
 * $17 \, 796 \, 126 \, 877 \, 482 \, 329 \, 126 \, 044 = 2^2 \times 7 \times 4327 \times 456 \, 293 \times 321 \, 911 \, 699 \, 243$

Thus: