Long division

Long division is a method for dividing numbers with multiple digits by hand. Below we see the notation that is used when doing long division.

This division problem is asking "how many times does 6 go into 564?" To find the answer, we perform long division as shown in the example below.

How to perform long division

  1. Reading from left to right, we first want to find the smallest sequence of digits (in the dividend, 564) that the divisor, 6, can go into at least once. 6 cannot go into the 5 in 564. Since it can't, move on to the next number formed, which is 56. 6 can go into 56 a total of 9 times to equal 54.

  2. Write the first value of the quotient above the dividend. In this case, write 9 above the 6 in 56 to indicate that 6 goes into 56 a total of 9 times. The position that the number 9 is written in is important. When doing long division, make sure that the numbers align. The starting point of the quotient should be above the last digit (reading from left to right) in the smallest sequence of numbers that the divisor can go into; in this case above the 6 in 56. The next number that forms the quotient should be written directly to the right of the first.

  3. Write the product, in this case 6 × 9 = 54, below 56, and perform subtraction; in this case there is a remainder of 2.

  4. Bring the 4 in 564 down next to the remainder to form 24, keeping in mind that alignment is important.

  5. Repeat the process starting from step 1, treating 24 as the new dividend. Continue this process as long as necessary until the remainder is 0, or we find a repeating pattern. In this case, since 6 × 4 = 24, subtract 24 from 24 to get 0, and the long division is complete. If, on a different problem, the remainder is not 0, continue to step 6.

  6. If there is still a remainder and there are no more new numbers from the dividend to bring down, add a decimal point and a 0, then bring the 0 down to the remainder and continue the process above (including adding 0's) until there is no longer a remainder, or until a repeating pattern is found.

For the above example, since the remainder is 0, the quotient is therefore 94, meaning that the solution to the problem 564 รท 6 is 94.

When the numbers do not divide exactly, we can either say the answer is the quotient and the remainder, or we can take the problem further with some extra steps to determine the solution using decimals. In some cases, we can find an exact solution, but in others, we can only approximate the value if the decimal does not terminate. Using an example similar to the one above, if the dividend were 566 instead of 564:

Following step 6, when we bring 0 down to the remainder of 2, we get 20. 6 goes into 20 a total of 3 times to get 18, resulting in a remainder of 2. No matter how many times we add and bring down a 0, the result will be the same, repeating decimal, so the quotient is 94.3, where the line above the 3 indicates that it repeats indefinitely.