If three numbers 112, 232, and 400 are each divided by the number D, each of their quotients will have the same remainder R. Find R where R>1
How should I approach this?
[Math] Find when three numbers have the same remainder when divided by the same number
elementary-number-theory
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Best Answer
Hint: $$112 - R \equiv 0 \mod D$$
$$232 - R \equiv 0 \mod D$$
$$400 - R \equiv 0 \mod D$$
$$120 \equiv 0 \mod D$$ $$168 \equiv 0 \mod D$$
Hence $D$ is a common factor of both $120$ and $168$.
$$24 \equiv 0 \mod D$$
$D \in \{1,2,3,4,6,8,12,24 \}$
Use $R>1$ to identify which $D$ is possible.