1. The problem is to perform long division for the first case: divide 3,678 by 5. 2. The formula for division is: $$\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}$$ 3. Start dividing the digits of 3,678 by 5 from left to right. 4. Divide 36 by 5: $$36 \div 5 = 7 \text{ remainder } 1$$ 5. Write 7 as the first digit of the quotient. 6. Bring down the next digit 7, making the new number 17. 7. Divide 17 by 5: $$17 \div 5 = 3 \text{ remainder } 2$$ 8. Write 3 as the next digit of the quotient. 9. Bring down the last digit 8, making the new number 28. 10. Divide 28 by 5: $$28 \div 5 = 5 \text{ remainder } 3$$ 11. Write 5 as the last digit of the quotient. 12. The quotient is 735 and the remainder is 3. 13. Verify: $$5 \times 735 + 3 = 3675 + 3 = 3678$$ which matches the dividend. Final answer: $$3,678 \div 5 = 735 \text{ remainder } 3$$