What is the smallest number that must be subtracted from 3000 to make the result exactly divisible by 17?

Explanation

1. 01

   Divide 3000 by 17 and look at the remainder rather than the quotient.

2. 02

   $17 \times 176 = 2992$, and $3000 - 2992 = 8$, so the remainder is 8.

3. 03

   Subtracting the remainder leaves an exact multiple: $3000 - 8 = 2992 = 17 \times 176$.

4. 04

   So 8 is the smallest number that works.