Long division for kids, step by step

Quick answer

Long division repeats four steps, one digit at a time: Divide (how many times does the divisor fit?), Multiply that digit by the divisor, Subtract, and Bring down the next digit. Repeat until no digits are left; anything remaining is the remainder. Check by multiplying the answer by the divisor and adding the remainder. Many schools teach it in 4th or 5th grade.

Long division has a scary reputation, but it's really one short routine repeated a few times. This guide explains each step with worked examples, the tricky cases (remainders, zeros, a small first digit), and the partial quotients method many schools teach first.

When do kids learn long division?

Here is the path under the Common Core, used by most U.S. states (your state or school may differ):

So the formal algorithm is a 6th-grade standard, yet many schools introduce it in 4th or 5th grade, often after a place-value method like partial quotients. Follow your child's teacher on which method comes first.

Is your child ready?

Long division uses three skills at once:

• Multiplication and division facts. Every step asks something like “how many 4s fit in 13?” If facts are slow, each problem becomes exhausting. Keep a multiplication chart on the table while facts are still settling.
• Subtraction with regrouping (borrowing). Every cycle includes a subtraction. Need a refresher? See subtraction with regrouping.
• Place value. Knowing that the 9 in 938 means 9 hundreds explains where each answer digit goes.

If division itself still feels new, start with how to teach division and come back here.

The four steps: divide, multiply, subtract, bring down

Let's work through 84 ÷ 4. The number being divided (84) is the dividend, the number you divide by (4) is the divisor, and the answer is the quotient. Write 84 under the long-division bracket and 4 outside it.

Step 1: Divide

Start with the first digit: how many 4s fit in 8? 2. Write 2 above the 8. (That 2 really means 2 tens, because 80 ÷ 4 = 20.)

Step 2: Multiply

Multiply the digit you just wrote by the divisor: 2 × 4 = 8. Write 8 under the 8.

Step 3: Subtract

8 − 8 = 0. The result must be smaller than the divisor. If it isn't, the digit from step 1 was too small.

Step 4: Bring down

Bring down the next digit, 4. Since nothing was left over, you now have just 4. Run the cycle again: 4 ÷ 4 = 1 (write 1 above the 4), 1 × 4 = 4, and 4 − 4 = 0.

214)84−84−40

Step 5: Repeat, then check

Keep cycling until there are no digits left to bring down. Then check with multiplication: quotient × divisor + remainder = dividend. Here, 21 × 4 = 84, so 84 ÷ 4 = 21 is right. A silly sentence like “Dad, Mom, Sister, Brother” can help your child remember the order: divide, multiply, subtract, bring down.

Worked examples: remainders, small first digits and zeros

A remainder: 938 ÷ 4

1. 9 ÷ 4 = 2. Multiply: 2 × 4 = 8. Subtract: 9 − 8 = 1. Bring down the 3 to make 13.
2. 13 ÷ 4 = 3. Multiply: 3 × 4 = 12. Subtract: 13 − 12 = 1. Bring down the 8 to make 18.
3. 18 ÷ 4 = 4. Multiply: 4 × 4 = 16. Subtract: 18 − 16 = 2. Nothing is left to bring down.

234R 24)938−813−1218−162

The 2 left at the end is the remainder: 938 ÷ 4 = 234 R2. Check: 234 × 4 = 936, and 936 + 2 = 938.

The first digit is too small: 156 ÷ 6

6 doesn't fit in 1, so look at the first two digits: 15. 15 ÷ 6 = 2, so write the 2 above the 5 (the tens place), not above the 1. Then 2 × 6 = 12, 15 − 12 = 3, and bring down the 6 to make 36. 36 ÷ 6 = 6, 6 × 6 = 36, 36 − 36 = 0.

266)156−1236−360

So 156 ÷ 6 = 26. Check: 26 × 6 = 156. Some teachers have kids write a 0 above the 1 as a placeholder at first; that's fine, as long as they read the answer as 26.

A zero in the quotient: 618 ÷ 3

1. 6 ÷ 3 = 2. 2 × 3 = 6. 6 − 6 = 0. Bring down the 1.
2. 1 ÷ 3 = 0, because 3 doesn't fit in 1. Write 0 in the quotient. 0 × 3 = 0, and 1 − 0 = 1. Bring down the 8 to make 18.
3. 18 ÷ 3 = 6. 6 × 3 = 18. 18 − 18 = 0.

2063)618−61−018−180

The answer is 206, not 26. A quick estimate catches that slip: 600 ÷ 3 = 200, so the answer must be about 200. Check: 206 × 3 = 618.

Partial quotients: the place-value method many schools teach first

The 4th-grade standard asks children to divide using strategies based on place value and the link between multiplication and division (4.NBT.B.6). Partial quotients does exactly that: take away easy multiples of the divisor, keep a tally of how many groups you took, and add them up at the end. Here is 938 ÷ 4 again:

Same answer: 234 R2. Any chunk your child knows works: taking away 10 × 4 = 40 again and again is slower, but still correct. Notice that the chunks (200, 30 and 4) match the digits of the long-division answer, which makes this method a natural bridge to the standard algorithm.

What to do with the remainder in word problems

In 4th grade, children solve word problems where they must decide what the remainder means (4.OA.A.3). Each of these is 30 ÷ 4 = 7 R2, but the answers differ:

• Round up: 30 kids ride in cars that hold 4. How many cars? 8, or 2 kids are left behind.
• Drop the remainder: 30 cookies go in bags of 4. How many full bags? 7.
• The remainder is the answer: 30 cards are dealt equally to 4 players. How many are left over? 2.
• Split the remainder: 30 inches of ribbon cut into 4 equal pieces. Each piece is 7 1/2 inches (fractions like this come later).

Always finish with: “Does the answer make sense in the story?”

Common long-division mistakes

• Skipping a zero in the quotient. 618 ÷ 3 written as 26. Rule of thumb: every time you bring down a digit, a digit goes up in the answer. Estimating first catches it.
• A remainder bigger than the divisor. If you subtract and get 5 while dividing by 4, another 4 fits. Make the answer digit 1 bigger.
• A product too big to subtract. If 5 × 4 = 20 can't be taken from 18, the digit is too big. Try one less.
• Starting the answer in the wrong place. In 156 ÷ 6, the first digit goes over the 5. Lining up digits by place keeps the answer the right size.
• Columns drifting. Use grid paper, or turn lined paper sideways so the lines become columns.
• Forgetting to check. Quotient × divisor + remainder should give back the dividend every time.

Practice problems

Start with two-digit dividends, then move to three and four digits. Have your child check each answer with multiplication.

Long division practice (with answers)

1. 96 ÷ 3 = ?
2. 72 ÷ 3 = ?
3. 85 ÷ 4 = ?
4. 135 ÷ 5 = ?
5. 504 ÷ 4 = ?
6. 412 ÷ 4 = ?
7. 749 ÷ 7 = ?
8. 527 ÷ 5 = ?
9. 1,236 ÷ 4 = ?
10. 3,145 ÷ 6 = ?
11. 29 kids, 4 per car: how many cars?

Show answers

For more practice, print our free division worksheets. Curious what else is on the list this year? See the 4th grade math skills checklist.

Frequently asked questions

What are the steps of long division?

Long division repeats four steps: divide (how many times does the divisor fit into the current number?), multiply (that digit times the divisor), subtract, and bring down the next digit. Keep cycling until there are no digits left to bring down; whatever is left is the remainder. Finish by checking: quotient × divisor + remainder should equal the number you started with.

What grade do kids learn long division?

Under the Common Core, 4th graders divide numbers up to four digits by one-digit numbers using place-value strategies (4.NBT.B.6), and 5th graders divide by two-digit numbers. Fluency with the standard long-division algorithm is listed as a 6th-grade standard (6.NS.B.2), but many schools teach the divide, multiply, subtract, bring down method in 4th or 5th grade.

What is the easiest way to teach long division to a beginner?

Make sure multiplication facts and subtraction with regrouping are solid first. Then start with two-digit numbers that divide evenly, like 84 ÷ 4, saying each step out loud. Use grid paper to keep columns straight and a multiplication chart for support. Add remainders, a small first digit and zeros in the answer one at a time.

How do you check a long division answer?

Multiply the quotient by the divisor, then add the remainder. The result should be the number you started with. For 938 ÷ 4 = 234 R2: 234 × 4 = 936, and 936 + 2 = 938, so the answer is right. A quick estimate catches big slips too: 938 ÷ 4 should be a little more than 800 ÷ 4 = 200.

What is the partial quotients method?

Partial quotients is a place-value way to divide. You subtract easy multiples of the divisor (like 100, 10 or 5 groups) from the dividend, write down how many groups you took each time, and add those numbers at the end. It gives the same answer as long division, lets children use facts they're confident with, and is often taught first.

Why does my child keep getting long division wrong?

The most common causes are slow multiplication facts, subtraction slips, columns that drift out of line, and skipped zeros in the answer. Watch your child do one problem out loud to find which step goes wrong. Then fix that one thing with a few short practice problems, and keep a multiplication chart handy while facts are still settling.

Sources

• Common Core State Standards: Grade 3, Operations & Algebraic Thinking — CCSSI
• Common Core State Standards: Grade 4, Operations & Algebraic Thinking — CCSSI
• Common Core State Standards: Grade 4, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 5, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 6, The Number System — CCSSI

Written by The Mathing Team for parents and teachers. Grade expectations follow the Common Core State Standards for Mathematics; your state or school may sequence skills a little differently.