BrightChamps Logo
Login

Summarize this article:

Live Math Learners Count Icon101 Learners

Last updated on August 26, 2025

Math Formula for Long Division

Professor Greenline Explaining Math Concepts

Long division is a method of dividing large numbers by breaking them down into a series of easier steps. It involves division, multiplication, and subtraction, following a specific sequence to obtain the quotient and remainder. In this topic, we will learn the formula for long division.

Math Formula for Long Division for US Students
Professor Greenline from BrightChamps

List of Steps in Long Division

Long division breaks down a division problem into a series of easier steps.

 

Let’s learn the systematic approach to perform long division.

Professor Greenline from BrightChamps

Steps for Long Division

Long division involves a sequence of steps: divide, multiply, subtract, bring down, and repeat until completion. The process is as follows:

 

1. Divide: Determine how many times the divisor fits into the current dividend portion.

 

2. Multiply: Multiply the divisor by the quotient found in the divide step.

 

3. Subtract: Subtract the result of the multiplication from the current dividend portion.

 

4. Bring down: Bring down the next digit of the dividend.

 

5. Repeat: Repeat the process until all digits have been used.

Professor Greenline from BrightChamps

Understanding the Components of Long Division

In long division, the dividend is the number being divided, the divisor is the number you are dividing by, the quotient is the result of the division, and the remainder is what is left over.

 

The formula for completing a division problem is: Dividend = (Divisor × Quotient) + Remainder

Professor Greenline from BrightChamps

Importance of Long Division

Long division is crucial in mathematics as it simplifies the division of large numbers:

 

- It provides a systematic method to obtain accurate results.

 

- It is foundational for understanding polynomial division and other advanced mathematical concepts.

 

- It aids in developing problem-solving skills and logical thinking.

Professor Greenline from BrightChamps

Tips and Tricks to Master Long Division

Students often find long division challenging, but with practice and some tricks, it can become easier:

 

- Break down the problem into smaller parts and focus on one step at a time.

 

- Practice using different numbers to become familiar with the process.

 

- Use estimation to quickly determine the quotient in each step.

 

- Double-check each subtraction step to ensure accuracy.

Professor Greenline from BrightChamps

Real-Life Applications of Long Division

Long division is used in various real-life scenarios to solve problems:

 

- Splitting a bill among friends to determine how much each person should pay.

 

- Dividing a quantity of items equally among groups.

 

- Calculating the average or finding proportions in recipes or construction projects.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them While Using Long Division

Students make errors when performing long division. Here are some mistakes and the ways to avoid them to master long division.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Incorrect initial division

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Sometimes students guess the wrong number of times the divisor fits into the dividend. To avoid this, use estimation and adjust as necessary.

Mistake 2

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Errors in multiplication or subtraction

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Mistakes often occur during multiplication or subtraction steps. Double-check each calculation to ensure accuracy.

Mistake 3

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting to bring down the next digit

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students might forget to bring down the next digit from the dividend, which can lead to incorrect results. Always remember to bring down digits in sequence.

Mistake 4

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Misplacing numbers in the quotient

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Numbers are sometimes misplaced in the quotient, leading to incorrect results. Carefully align each new quotient digit above the corresponding dividend digit.

arrow-right
Max from BrightChamps Saying "Hey"
Hey!

Examples of Problems Using Long Division

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Divide 125 by 5 using long division.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

The quotient is 25

Explanation

1. Divide: 5 goes into 12 twice (2), since 5 x 2 = 10

 

2. Subtract: 12 - 10 = 2

 

3. Bring down the next digit: 5, making it 25

 

4. Divide: 5 goes into 25 five times (5), since 5 x 5 = 25

 

5. Subtract: 25 - 25 = 0 Therefore, 125 ÷ 5 = 25.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

Problem 2

Divide 364 by 4 using long division.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

The quotient is 91

Explanation

1. Divide: 4 goes into 36 nine times (9), since 4 x 9 = 36

 

2. Subtract: 36 - 36 = 0

 

3. Bring down the next digit: 4

 

4. Divide: 4 goes into 4 once (1), since 4 x 1 = 4

 

5. Subtract: 4 - 4 = 0

 

Therefore, 364 ÷ 4 = 91.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

Problem 3

Divide 729 by 3 using long division.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

The quotient is 243

Explanation

1. Divide: 3 goes into 7 twice (2), since 3 x 2 = 6

 

2. Subtract: 7 - 6 = 1

 

3. Bring down the next digit: 2, making it 12

 

4. Divide: 3 goes into 12 four times (4), since 3 x 4 = 12

 

5. Subtract: 12 - 12 = 0

 

6. Bring down the next digit: 9

 

7. Divide: 3 goes into 9 three times (3), since 3 x 3 = 9

 

8. Subtract: 9 - 9 = 0

 

Therefore, 729 ÷ 3 = 243.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Ray Thinking Deeply About Math Problems

FAQs on Long Division Formula

1.What is the basic formula for long division?

The basic formula for long division is: Dividend = (Divisor × Quotient) + Remainder

Math FAQ Answers Dropdown Arrow

2.How do you perform long division?

To perform long division, follow these steps: divide, multiply, subtract, bring down, and repeat until all digits of the dividend have been used.

Math FAQ Answers Dropdown Arrow

3.What do you do if there is a remainder?

If there is a remainder, it is included in the final answer as a leftover part of the division or continued as a decimal.

Math FAQ Answers Dropdown Arrow

4.Why is long division important?

Long division is important because it provides a systematic approach to dividing large numbers accurately and is foundational for more complex mathematics.

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Glossary for Long Division Formula

  • Dividend: The number being divided in a division problem.

     
  • Divisor: The number by which the dividend is divided.

     
  • Quotient: The result obtained from a division.

     
  • Remainder: The leftover part of the dividend that cannot be evenly divided by the divisor.

     
  • Estimation: A method of finding an approximate answer, often used to simplify calculations in long division.
Math Teacher Background Image
Math Teacher Image

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
UAE - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom