Hmm, that's not much

$\begin{aligned} 15876000 & = 32 × 81 × 125 × 49\\ & = 2^\color{#20A900}{5} × 3^\color{#20A900}{4} × 5^\color{#20A900}{3} × 7^\color{#20A900}{2} \end{aligned}$

So, we can make the number of factors by combining the powers. For each power ww have $(n + 1)$ options. (1 is added because we can even choose not to take them at all. Note that if we dont choose any of them we still get a factor "1").

So, the total number of factors that are possible = $(5+1)(4+1)(3+1)(2+1) = 6×5×4×3 = \color{#3D99F6}{\boxed{360}}$ .