Compare with the example $10$ from the handout:

 All of $47$, $98$ and $183$ leave the same remainder $R$ when divided by $D$. This means all of them look like $D\times k + R$ for some integer $k$. Thus, the difference of any two of them will be a multiple of $D$: $98-47 = 51$, $183-98 = 85$ and $183-47 = 136$. The GCD of $51$, $85$ and $136$ is $17$, so $D$ should be either $1$ or $17$, but since $D>1$, $D=17$.