When z is divided by 8, the remainder is 5. What is the remainder when 4z is divided by 8?

The question states that z divided by 8, or z/8 has a remainder of 5. That means that 8 goes into z 5 times, but has a remainder of 5, meaning that 8*5+5=z=45. To find 4z, we multiply 45 by 4 to get 180. Next, we use long division to divide that by 8.

     22
   ______
8 | 180
     -160
     ____
       20
       -16
       ___
          4. This can be done due to that 8 does not go into 1, but 8*2=16, and 8*3=24. Keep in mind that since 8 doesn't go into 1, the 1 moves over with the 8 to form 18. Next, we have 18-16=2, and we add a 0 at the end because 180 has 3 digits. We repeat the process for 20, and at the end, since 8 does not go into 4, we have a remainder of 4