Long Division with Remainders

A remainder is what is left when a division problem does not divide evenly. Learn how to find it, write it, and check that your answer is correct.

What Is a Remainder?

A remainder is the amount left after making as many full groups as possible.

For example, 17 ÷ 5 = 3 R2. The number 5 fits into 17 three full times. Then 3 × 5 = 15, and 17 − 15 = 2. So the remainder is 2.

Key rule

Remainder < Divisor

How to Write a Remainder

The remainder is written after the quotient using R notation.

Quotient 3
Remainder 2

In 17 ÷ 5 = 3 R2, 3 is the quotient and 2 is the remainder.

In 157 ÷ 4 = 39 R1, R1 means 1 is left after 39 complete groups of 4.

Need a refresher on the full method? How to Do Long Division Step by Step

Find the Final Remainder

Example 1: 157 ÷ 4

157 ÷ 4 = 39 R1

      39
   -----
4 ) 157
    12
    --
     37
     36
     --
      1
  1. 4 goes into 15 three times.
  2. 3 × 4 = 12.
  3. Subtract to get 3, then bring down 7.
  4. 4 goes into 37 nine times.
  5. 9 × 4 = 36.
  6. 37 − 36 = 1.
  7. There are no more digits to bring down, so 1 is the remainder.

Another Remainder Example

Example 2: 116 ÷ 5

116 ÷ 5 = 23 R1

      23
   -----
5 ) 116
    10
    --
     16
     15
     --
      1

Once there are no more digits to bring down, stop if the remainder is smaller than the divisor.

Here 1 is smaller than 5, so the answer is 23 R1.

Remainders with a Multi-Digit Divisor

Example 3: 8576 ÷ 111

8576 ÷ 111 = 77 R29

        77
    ------
111 ) 8576
      777
      ---
       806
       777
       ---
        29

A remainder does not have to be a single digit. It only has to be smaller than the divisor.

Here 29 is a valid remainder because 29 < 111.

How to Check a Long Division Answer

Use the quotient, divisor, and remainder to rebuild the dividend.

Quotient × Divisor + Remainder = Dividend

Check 157 ÷ 4 = 39 R1

39 × 4 + 1
= 156 + 1
= 157

Check 8576 ÷ 111 = 77 R29

77 × 111 + 29
= 8547 + 29
= 8576

When Is a Remainder Wrong?

  • The remainder is too large: 17 ÷ 5 = 2 R7 is wrong because 7 ≥ 5. You can still make one more full group, so the correct answer is 3 R2.
  • The arithmetic does not check: If quotient × divisor + remainder does not equal the dividend, the answer needs to be corrected.

Remainder or Decimal?

Whole-number division often writes answers with a remainder: 157 ÷ 4 = 39 R1.

The same value can also be written as a decimal: 39.25. This page focuses on remainder notation.

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FAQ

What is a remainder in division?

A remainder is the amount left after making as many full groups as possible.

Can a remainder be bigger than the divisor?

No. If the remainder is bigger than the divisor, you can make another full group.

Can the remainder equal the divisor?

No. If the remainder equals the divisor, add 1 to the quotient and make the remainder 0.

How do I check a remainder?

Use quotient × divisor + remainder. The result should equal the dividend.

What does R1 mean in a division answer?

R1 means remainder 1, so 1 is left after the full groups are made.

Can a remainder be written as a decimal?

Yes. A remainder can represent the same value as a decimal or fraction, but the notation is different.