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Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

For how many positive integers $N$ is the remainder $6$ when $111$ is divided by $N$ ?

(A) $5$ (B) $4$ (C) $3$ (D) $2$ (E) $1$

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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) added by this project. Solutions are the publisher's, linked not copied.