Find when three numbers have the same remainder when divided by the same number 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?

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.
