Long Division Problem: Dividing 2831 by 5 Step-by-Step

To solve this problem, we'll use long division to divide 2831 by 5:

• Step 1: Divide the first digit of the dividend (2) by 5. Since 2 is less than 5, use the first two digits (28).
• Step 2: 5 goes into 28 five times (because $5 \times 5 = 25$), so place 5 in the quotient.
• Step 3: Subtract 25 from 28, resulting in a remainder of 3. Bring down the next digit (3) to get 33.
• Step 4: 5 goes into 33 six times (because $5 \times 6 = 30$), so place 6 in the quotient.
• Step 5: Subtract 30 from 33, resulting in a remainder of 3. Bring down the next digit (1) to get 31.
• Step 6: 5 goes into 31 six times (because $5 \times 6 = 30$), so place another 6 in the quotient.
• Step 7: Subtract 30 from 31, resulting in a final remainder of 1.

The complete quotient is 566 with a remainder of 1.

Therefore, the correct answer is the option: $566$ with a remainder of 1.