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The number $315$ can be written as the product of two odd integers each greater than $1$. In how many ways can this be done?

(A) $0$ (B) $1$ (C) $3$ (D) $4$ (E) $5$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.