Long Division Examples: 48 Problems with Answers

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 \div 6

Answer

141

First step

Divide 8 by 6: quotient digit 1, remainder

8 - 6 = 2

. Bring down 4 to get 24.

Full solution

2
Divide 24 by 6: quotient digit 4, remainder 0. Bring down 6 to get 6.
3
Divide 6 by 6: quotient digit 1, remainder 0.
4
Result: $846 \div 6 = 141$ .

Long division works digit by digit from left to right: divide, multiply, subtract, bring down, and repeat.

Example 2

medium

Compute

1573 \div 11

Example 3

easy

Compute

988 \div 4

step by step.

Example 4

medium

A teacher has

1326

pencils to share equally among

13

classes. How many pencils per class?

Example 5

hard

A car travels

432

miles on

18

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 \div 7

Example 2

hard

Compute

2034 \div 12

Example 3

easy

Compute

84 \div 4

Example 4

easy

Compute

96 \div 3

Example 5

easy

Compute

17 \div 5

, giving quotient and remainder.

Example 6

easy

Compute

63 \div 7

Example 7

easy

Compute

40 \div 8

Example 8

easy

Compute

25 \div 4

, quotient and remainder.

Example 9

easy

Compute

100 \div 4

Example 10

easy

Compute

72 \div 6

Example 11

medium

Compute

156 \div 12

using long division.

Example 12

medium

Compute

245 \div 7

Example 13

medium

Compute

329 \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 \div 8

Example 16

medium

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

Example 17

medium

Express

47 \div 4

as a mixed number.

Example 18

medium

Compute

408 \div 8

Example 19

medium

Compute

500 \div 6

, quotient and remainder.

Example 20

challenge

Compute

4321 \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 \div 9

Example 24

easy

Compute

369 \div 9

Example 25

easy

Compute

144 \div 12

Example 26

easy

Compute

504 \div 8

Example 27

medium

Compute

1234 \div 6

, giving quotient and remainder.

Example 28

medium

Compute

7250 \div 25

Example 29

medium

Compute

4500 \div 15

Example 30

medium

Compute

2856 \div 14

Example 31

medium

Compute

999 \div 11

, quotient and remainder.

Example 32

medium

Compute

3024 \div 18

Example 33

medium

Compute

8125 \div 25

Example 34

medium

Compute

4096 \div 16

Example 35

medium

Compute

2025 \div 15

Example 36

hard

Compute

6543 \div 21

, quotient and remainder.

Example 37

hard

Compute

1000 \div 32

, quotient and remainder.

Example 38

hard

Compute

9999 \div 11

Example 39

hard

Compute

12345 \div 5

Example 40

hard

Compute

250 \div 6

, quotient and remainder.

Example 41

hard

Compute

1080 \div 27

Example 42

challenge

When a number

N

is divided by

17

, the quotient is

58

and the remainder is

9

. Find

N

Example 43

challenge

Find the largest three-digit number divisible by

23

← Back to Long Division Formula Explained Practice Mode

Related Concepts

Division Subtraction Multiplication Dividing Decimals

Background Knowledge

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

divisionsubtractionmultiplication