A Problematic Factorization Problem

$\begin{aligned} 27000001 & = \; 300^3 + 1 \; = \; (300 + 1)(300^2 - 300 + 1) \; = \; 301 \times \big(300^2 + 2\times300 + 1 - 900\big) \; = \; 301 \times \big(301^2 - 30^2\big) \\ & = \; 7 \times 43 \times 271 \times 331 \end{aligned}$ making the answer $\boxed{331}$ .