How to Find the Quotient and Remainder Using Long Division

Long division is a handwritten way to perform the algebraic operation of division. A number called a dividend is placed under a bracket while the number dividing into it (called the divisor) is placed off to the left. You work from left to right, trying to divide the divisor into each digit(s) of the dividend. Answers go on top of the bracket directly above the spot they provide the solution to. When you run out of numbers to drop down, you can either add zeros to the end and keep going to find the full decimal answer or write out the leftover number as a remainder.


    • 1

      Find the quotient of two numbers using long division by placing the dividend under the bracket and the divisor out to the left. Work on dividing the divisor into the dividend, step by step, placing answers above the bracket and dropping down the next dividend number when needed. Stop when you reach the end of your dividend and write the leftovers as a remainder on the answer.

    • 2

      For example, divide 212 by 15 and write the answer with remainders. Write the 212 beneath the bracket and write 15 off to the left. Begin dividing 15 into 212 by moving digit by digit and determining whether it's possible. Check whether 15 divides into the first digit and it does not. Write a 0 on the line above the 2. Check whether 15 divides into 21 and it does one time. Write a 1 on the line above the 1 and subtract 15 from the 21 = 21 - 15 = 6.

    • 3

      Drop down the final 2 in 212 to join the 6 remaining to make 62. Decide how many times 15 goes into 62 and then write 4 on the line above the 2. Subtract 60 from the 62: 62 - 60 = 2. Note that there are no more numbers in the dividend, so this is a remainder.

    • 4

      Write your answer as 212 ÷ 15 = 14 R 2.

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