May 04, 2023

Long Division - Steps, Examples

Long division is a crucial math concept which has many real-world uses in different domains. One of its primary application is in finance, where it is used to calculate interest rates and find out loan payments. It is also utilized to work out investments, budgeting, and taxes, making it an important skill for anyone engaged in finance.

In engineering, long division is used to solve intricate problems in connection to construction, design, and development. Engineers use long division to estimate the loads that structures can endure, assess the strength of materials, and plan mechanical networks. It is also used in electrical engineering to calculate circuit parameters and design complicated circuits.

Long division is also crucial in science, where it is used to calculate measurements and execute scientific workings. Such as astronomers utilize long division to calculate the distances between stars, and physicists use it to figure out the velocity of objects.

In algebra, long division is utilized to factor polynomials and solve equations. It is a crucial tool for working out complicated problems that include large numbers and need precise calculations. It is also used in calculus to calculate derivatives and integrals.

As a whole, long division is an important mathematical theory that has several practical applications in several domains. It is a rudimental arithmetic operation that is used to work out complicated problems and is an essential skill for anyone interested in science, finance, engineering, or arithmetic.

Why is Long Division Important?

Long division is an important mathematical concept that has many applications in different fields, consisting of finance, engineering, and science. It is a fundamental math function that is applied to figure out a broad spectrum of problems, for instance, working out interest rates, determining the length of time needed to complete a project, and figuring out the length traveled by an object.

Long division is further used in algebra to factor polynomials and solve equations. It is an important tool for solving complex problems that include huge values and need exact calculations.

Stages Involved in Long Division

Here are the procedures involved in long division:

Step 1: Write the dividend (the number being divided) on the left and the divisor (the number dividing the dividend) on the left.

Step 2: Calculate how many times the divisor could be divided into the first digit or set of digits of the dividend. Note down the quotient (the outcome of the division) above the digit or set of digits.

Step 3: Multiply the quotient by the divisor and note down the result below the digit or set of digits.

Step 4: Subtract the outcome achieved in step 3 from the digit or set of digits in the dividend. Note down the remainder (the amount left over after the division) below the subtraction.

Step 5: Carry down the following digit or set of digits from the dividend and append it to the remainder.

Step 6: Replicate steps 2 to 5 unless all the digits in the dividend have been processed.

Examples of Long Division

Here are handful of examples of long division:

Example 1: Divide 562 by 4.




4 | 562







Thus, 562 divided by 4 is 140 with a remainder of 2.

Example 2: Divide 1789 by 21.




21 | 1789







Thus, 1789 divided by 21 is 85 with a remainder of 11.

Example 3: Divide 3475 by 83.




83 | 3475







Therefore, 3475 divided by 83 is 41 with a remainder of 25.

Common Mistakes in Long Division

Long division can be a difficult idea to master, and there are many common errors which learners make when performing long division. One usual mistake is to forget to note down the remainder when dividing. One more common mistake is to incorrectly put the decimal point when dividing decimal numbers. Learners may also forget to carry over figures while subtracting the product from the dividend.

To avoid making these mistakes, it is important to work on long division frequently and ready carefully ever stage of the procedure. It can further be helpful to check your calculations using a calculator or by working the division in reverse to assure that your answer is right.

Additionally, it is important to get a grasp of the rudimental principles about long division, for example, the relationship between the quotient, dividend, divisor, and remainder. By mastering the basics of long division and avoiding common errors, individuals can enhance their abilities and obtain confidence in their ability to solve complicated problems.


In conclusion, long division is an essential mathematical theory that is important for figuring out complex challenges in many fields. It is utilized in finance, engineering, science, and mathematics, making it an important ability for working professionals and students alike. By conquering the procedure involved in long division and comprehending how to utilize them to real-world challenges, individuals can gain a deeper understanding of the complicated functions of the world around us.

If you want help comprehending long division or any other arithmetic concept, Grade Potential Tutoring is here to help. Our expert instructors are available remotely or face-to-face to provide personalized and effective tutoring services to support you be successful. Our instructors can assist you through the stages in long division and other math ideas, assist you work out complex problems, and provide the tools you need to excel in your studies. Connect with us today to plan a tutoring session and take your math skills to the next level.