Long Division Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Long Division.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Long division is a step-by-step method for dividing large numbers by breaking the problem into a series of easier steps: divide, multiply, subtract, bring down, and repeat. It produces a quotient and possibly a remainder.

Long division is like distributing items into groups one place value at a time. If you have 156 stickers to share among 12 friends, you first figure out how many groups of 12 fit in 156 by working from the biggest place value down: how many 12s in 15? Then bring down the next digit and repeat.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Long division is a controlled way to remove equal-size groups one place value at a time.

Common stuck point: The procedure for long division is the easy part; the trap is dropping a digit without asking what place it represents. Asking "Can I check the answer by multiplying the quotient by the divisor?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Can I check the answer by multiplying the quotient by the divisor?

Worked Examples

Example 1

easy
Compute 846÷6846 \div 6.

Answer

141141

First step

1
Divide 8 by 6: quotient digit 1, remainder 8−6=28 - 6 = 2. Bring down 4 to get 24.

Full solution

  1. 2
    Divide 24 by 6: quotient digit 4, remainder 0. Bring down 6 to get 6.
  2. 3
    Divide 6 by 6: quotient digit 1, remainder 0.
  3. 4
    Result: 846÷6=141846 \div 6 = 141.
Long division works digit by digit from left to right: divide, multiply, subtract, bring down, and repeat.

Example 2

medium
Compute 1573÷111573 \div 11.

Example 3

easy
Compute 988÷4988 \div 4 step by step.

Example 4

medium
A teacher has 13261326 pencils to share equally among 1313 classes. How many pencils per class?

Example 5

hard
A car travels 432432 miles on 1818 gallons. Find the miles per gallon.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
Compute 952÷7952 \div 7.

Example 2

hard
Compute 2034÷122034 \div 12.

Example 3

easy
Compute 84÷484 \div 4.

Example 4

easy
Compute 96÷396 \div 3.

Example 5

easy
Compute 17÷517 \div 5, giving quotient and remainder.

Example 6

easy
Compute 63÷763 \div 7.

Example 7

easy
Compute 40÷840 \div 8.

Example 8

easy
Compute 25÷425 \div 4, quotient and remainder.

Example 9

easy
Compute 100÷4100 \div 4.

Example 10

easy
Compute 72÷672 \div 6.

Example 11

medium
Compute 156÷12156 \div 12 using long division.

Example 12

medium
Compute 245÷7245 \div 7.

Example 13

medium
Compute 329÷5329 \div 5, quotient and remainder.

Example 14

medium
156 stickers are shared equally among 12 friends. How many does each get?

Example 15

medium
Compute 1000÷81000 \div 8.

Example 16

medium
A bus seats 48 people. How many buses are needed for 290 people?

Example 17

medium
Express 47÷447 \div 4 as a mixed number.

Example 18

medium
Compute 408÷8408 \div 8.

Example 19

medium
Compute 500÷6500 \div 6, quotient and remainder.

Example 20

challenge
Compute 4321÷74321 \div 7, giving quotient and remainder, then verify.

Example 21

challenge
When a number is divided by 9 the quotient is 12 and the remainder is 5. What is the number?

Example 22

challenge
Find the smallest number greater than 200 that is divisible by 13.

Example 23

easy
Compute 567÷9567 \div 9.

Example 24

easy
Compute 369÷9369 \div 9.

Example 25

easy
Compute 144÷12144 \div 12.

Example 26

easy
Compute 504÷8504 \div 8.

Example 27

medium
Compute 1234÷61234 \div 6, giving quotient and remainder.

Example 28

medium
Compute 7250÷257250 \div 25.

Example 29

medium
Compute 4500÷154500 \div 15.

Example 30

medium
Compute 2856÷142856 \div 14.

Example 31

medium
Compute 999÷11999 \div 11, quotient and remainder.

Example 32

medium
Compute 3024÷183024 \div 18.

Example 33

medium
Compute 8125÷258125 \div 25.

Example 34

medium
Compute 4096÷164096 \div 16.

Example 35

medium
Compute 2025÷152025 \div 15.

Example 36

hard
Compute 6543÷216543 \div 21, quotient and remainder.

Example 37

hard
Compute 1000÷321000 \div 32, quotient and remainder.

Example 38

hard
Compute 9999÷119999 \div 11.

Example 39

hard
Compute 12345÷512345 \div 5.

Example 40

hard
Compute 250÷6250 \div 6, quotient and remainder.

Example 41

hard
Compute 1080÷271080 \div 27.

Example 42

challenge
When a number NN is divided by 1717, the quotient is 5858 and the remainder is 99. Find NN.

Example 43

challenge
Find the largest three-digit number divisible by 2323.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

divisionsubtractionmultiplication