How to Do Long Division: Step-by-Step With Examples

Long division breaks a big division problem into a series of small ones. You repeat the same four steps, divide, multiply, subtract, bring down, working left to right through the dividend one digit at a time. For example, 7,632 ÷ 6 = 1,272, found by dividing 7, then 16, then 43, then 12 by 6 in turn.

Before starting, it helps to know the vocabulary:

The four-step cycle

1. Divide. Ask how many times the divisor fits into the current number. Write that digit in the quotient.
2. Multiply. Multiply the divisor by that digit.
3. Subtract. Subtract the product from the current number. The result must be smaller than the divisor; if it is not, your quotient digit was too small.
4. Bring down. Bring down the next digit of the dividend beside the remainder to form the next number.

Repeat until there are no digits left to bring down. Whatever remains is the remainder.

Example 1: one-digit divisor (7,632 ÷ 6)

Reading the quotient digits from top to bottom gives 1,272, with no remainder. Check: 1,272 × 6 = 7,632.

Example 2: two-digit divisor (9,875 ÷ 23)

Two-digit divisors work the same way, but finding each quotient digit takes an estimate. Round the divisor to make the guess easy, then adjust.

Since 23 does not fit into 9, start with the first two digits, 98.

The answer is 429 remainder 8, written 429 R 8. Check: 429 × 23 = 9,867, and 9,867 + 8 = 9,875.

Notice the adjustment in the second row. When a product comes out larger than the current number, lower the quotient digit by one. When the subtraction leaves a remainder equal to or larger than the divisor, raise it by one. A quick list of the divisor’s multiples (23, 46, 69, 92, 115, …) makes this fast, and the long multiplication calculator helps if the products get large.

Example 3: zeros in the quotient (4,218 ÷ 7)

The answer is 602 R 4. The middle step is where most errors happen: when the divisor does not fit, you must still write a 0 in the quotient before bringing down the next digit. Leaving it out would give 62, which is off by a factor of ten. A quick estimate catches this: 4,218 ÷ 7 should be roughly 4,200 ÷ 7 = 600.

What to do with the remainder

A remainder can be written three ways, and the right one depends on the question.

• As a remainder: 429 R 8.
• As a fraction: put the remainder over the divisor. 429 8/23.
• As a decimal: keep dividing past the decimal point. 429.35 to two places.

In word problems, the context decides. If 9,875 bottles are packed 23 to a case, you fill 429 full cases with 8 bottles left over, but you need 430 cases to hold every bottle. More examples like this are on the division word problems page.

Long division with decimals

Continuing past the decimal point

To get a decimal answer instead of a remainder, place a decimal point after the dividend, write one directly above it in the quotient, and bring down zeros.

Some divisions never end. 5 ÷ 6 gives 0.8333…, because the remainder 2 keeps returning. Once a remainder repeats, the digits that follow repeat too, so you can stop and mark the repeating part. The long division with decimals calculator detects repeating decimals automatically.

Dividing by a decimal

Long division needs a whole-number divisor. Multiply both numbers by the same power of 10 to clear the divisor’s decimal point:

For 15.6 ÷ 0.4, shift both decimal points one place: 156 ÷ 4 = 39. The answer does not change because you scaled both numbers equally.

Checking your work

Every long division can be verified with one line of multiplication: quotient × divisor + remainder should equal the dividend. It takes seconds and catches nearly every mistake. An estimate first is also worth the effort; knowing that 9,875 ÷ 23 should be a little over 400 (since 23 × 400 = 9,200) tells you at once if you have dropped or added a digit.

Common mistakes

• Forgetting a zero in the quotient when the divisor does not fit.
• Misaligning digits, so a quotient digit sits over the wrong place value.
• A remainder that is too big. If any subtraction leaves a number equal to or larger than the divisor, the quotient digit should be one higher.
• Bringing down two digits at once. Bring down exactly one digit per cycle, writing a 0 in the quotient if needed.

If you only need the remainder, as in clock arithmetic or checking divisibility, the modulo calculator returns it directly. To see any problem worked out in full, enter it in the long division calculator. For turning a fraction into a decimal, which is long division in disguise, see how to convert a decimal to a fraction for the reverse direction.