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When $180$ is divided by a positive integer $N$, the remainder is $5$. For how many values of $N$ is this true? (A) $4$ (B) $5$ (C) $6$ (D) $7$ (E) $8$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.