Long Division Worksheets: 3-Digit by 1-Digit

Long division 3-digit by 1-digit uses the same four steps as 2-digit problems, with one more round, and two new things to watch for: a first digit that is too small, and a zero in the answer. The four PDFs on this page have problems that divide evenly, problems with remainders and a mixed set, and every answer key shows each step. They follow standard 4.NBT.B.6 of the Common Core standards for grade 4 number and operations in base ten.

About these worksheets

Three-digit long division uses the same four steps as 2-digit problems, repeated one more time. Two things catch children out:

• The first digit is too small: in 256 ÷ 4, 4 does not go into 2, so start with 25. The answer has only two digits.
• A zero in the answer: in 408 ÷ 4, after 4 ÷ 4 = 1, bring down the 0. 4 goes into 0 zero times, so write 0 in the answer before bringing down the 8. The answer is 102, not 12.

What is on this page

• Problems that divide evenly.
• Problems that all have remainders.
• A mixed set.

Long division 3-digit by 1-digit worksheets: what is in the set

There are 4 long division 3-digit by 1-digit worksheets on this page, and every one has an answer key except for any cut-out games. Two sets have problems that divide evenly, one has problems with remainders, and one is a mix.

3 digit by 1 digit division worksheets: how the sets are built

The 3 digit by 1 digit division worksheets in this pack have four sets with twelve problems each. Two sets divide evenly, one set has a remainder in every problem, and one set is a mix of both. The problems use divisors from 2 to 9 and dividends from 100 to 999, and every answer key shows each round of the division, including the rounds where a zero goes in the answer.

Long division 3-digit by 1-digit: four worked examples

Long division 3-digit by 1-digit has three rounds of the four steps, and the number we divide in the first round can be one digit or two. These tables show the steps for four problems that cover the cases children meet most. Wikipedia’s article on long division has a full description. The first is an easy problem with no remainder:

456 ÷ 3 = 152

The second has a first digit that is too small, since 4 does not go into 2:

256 ÷ 4 = 64

The third has a zero in the answer, because after 4 − 4 = 0 the next digit is 0:

408 ÷ 4 = 102

The fourth has a remainder, and it also has a zero in the answer:

725 ÷ 6 = 120 R5

3 digit division: how many digits will the answer have?

For 3 digit division, the number of digits in the answer depends on the first digit of the dividend. If the first digit is smaller than the divisor, the answer has two digits. If it is as big as the divisor, the answer has three. This table counts the three-digit dividends from 100 to 999 for each divisor from 2 to 9:

With a divisor of 2 most dividends have a three-digit answer, but with a divisor of 9 only the numbers from 900 to 999 do. A zero in the answer is also common: for a divisor of 4, about one dividend in 6 has a 0 in the answer. The share in the table is the reason why the zero needs its own practice.

Zeros in the answer: when the divisor does not go in

A zero in the answer appears when the number we divide in some round is smaller than the divisor. Children often skip the round and write an answer that is a digit short. This table shows the first dividends that divide evenly and have a 0 in the answer, for four divisors:

The rule is that every digit of the dividend has a matching digit in the answer, starting from the first digit that the divisor can go into. If a digit has no matching digit in the answer, the answer is wrong. The place value worksheets page explains the place of each digit.

Long division with remainders: every remainder is equally likely

For long division with remainders, there is a surprise for children who ask how often each remainder appears. Among the 900 three-digit dividends, each remainder comes up almost exactly the same number of times. This table shows the counts for five divisors:

For a divisor of 6, every remainder from 0 to 5 appears exactly 150 times, because 900 is a multiple of 6. For 7, the counts are 128 or 129. This is the reason why one worksheet cannot have only problems with the same remainder. The division with remainders page explains what a remainder means in a story.

Long division worksheets grade 4: estimating first

The long division worksheets grade 4 expect children to estimate before dividing, using compatible numbers. A compatible number is one that is close to the dividend and easy to divide, such as 720 for 725 when the divisor is 6. This table shows six estimates, with the exact answer:

An estimate does not need to be exact, and it is a way to catch a missing digit. If the estimate of 725 ÷ 6 is 120 and the answer is 12, the answer is wrong. The estimating with rounding page has more about estimating.

Long division practice: checking every answer

Long division practice is easier when children check every answer. The check is to multiply the answer by the divisor and add the remainder. This table checks six answers from the examples above:

The check also shows why the remainder must be smaller than the divisor. If it is as big as the divisor, another group fits, and the answer is one digit short in the last place.

Common mistakes with long division 3-digit by 1-digit

Most mistakes come from the first digit, from a missing zero, or from a column that is not lined up. This table shows five mistakes, what went wrong and the fix:

Long division 3-digit by 1-digit word problems

Story problems for three-digit division use packing and sharing. Ask children to estimate first, solve with the four steps and then check:

Games and activities for long division 3-digit by 1-digit

Children learn long division 3-digit by 1-digit best when they play with it. These games use things that are found at home or in a classroom:

• Estimate and check: estimate the answer with a compatible number before every problem
• Zero detective: find problems in a set that have a zero in the answer before solving them
• Remainder bingo: a bingo card with remainders, and calling cards with problems
• Digit cards: draw three digit cards and a divisor card, and divide the three-digit number
• Check partner: swap worksheets and check each answer by multiplying
• Packing contest: find how many full boxes of 6 can be made from 725 counters, using a calculator to check

Extra support and extra challenge with long division 3-digit by 1-digit

For children who need more support: write the multiples of the divisor beside the problem, and make sure the 2-digit long division is secure first. Use grid paper to keep the digits in columns. Mark where each digit of the answer goes before starting, and use the answer key to check every round.

For children who need more challenge: ask for the answer to 2,000 ÷ 8 using the zeros, for the biggest 3-digit number that divides by 7 with a remainder of 6, and for the dividend with the answer 105 when divided by 6. Look for dividends that give a zero in the answer, and make up a story for one of them.

How to tell that a child is ready to move on from long division 3-digit by 1-digit

1. The child places the first digit of the answer correctly.
2. The child writes a zero in the answer when the divisor does not go in.
3. The child finds the remainder and checks that it is smaller than the divisor.
4. The child estimates and checks every answer.

When all four are true, long division 3-digit by 1-digit is secure, so move on to the long division 4-digit by 1-digit page, or to the long division 2-digit divisors page.

A 20-minute lesson on long division 3-digit by 1-digit

A short lesson is the best way to introduce long division 3-digit by 1-digit. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where long division 3-digit by 1-digit fits across the grades

No skill stands alone. This table shows what children learn before and after long division 3-digit by 1-digit, with the standard that goes with each step:

This page is the center of the long division sequence. The whole sequence is on the long division worksheets page.

Helping at home with long division 3-digit by 1-digit

Parents do not need to be experts to help with long division 3-digit by 1-digit. These suggestions work well, and each takes only a few minutes:

• Ask the child to estimate the answer before dividing.
• Use real numbers, such as dividing 365 days into weeks.
• Ask “does the divisor go into this digit?” at every round.
• Check each answer by multiplying and adding the remainder.
• Keep a card with the four steps next to the homework.

How to check progress in long division 3-digit by 1-digit

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for long division 3-digit by 1-digit

Most children need about a week of short sessions for long division 3-digit by 1-digit. This plan follows the order of the worksheets on this page:

When the plan for long division 3-digit by 1-digit is complete, move on to the long division 4-digit by 1-digit page. The whole sequence is on the long division worksheets page.