May 04, 2023

Long Division - Steps, Examples

Long division is an important mathematical concept which has multiple real-world utilizations in different fields. One of its primary uses is in finance, where it is used to figure out interest rates and work out loan payments. It is further used to figure out investments, budgeting, and taxes, making it an essential skill for everyone engaged in finance.

In engineering, long division is applied to solve complex challenges in connection to construction, design, and development. Engineers use long division to calculate the loads which structures can hold, assess the strength of materials, and plan mechanical systems. It is further applied in electrical engineering to determine circuit parameters and design intricate circuits.

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

In algebra, long division is used to factor polynomials and solve equations. It is a crucial tool for solving complicated challenges that involve huge numbers and need accurate calculations. It is also utilized in calculus to calculate derivatives and integrals.

As a whole, long division is a crucial math concept which has many real-life applications in many domains. It is a fundamental math operation which is utilized to figure out complex problems and is an essential skill for everyone interested in finance, engineering, science, or arithmetic.

Why is Long Division Important?

Long division is an essential math idea that has numerous applications in different fields, including finance, engineering, and science. It is an essential mathematics operation which is used to solve a wide array of challenges, for example, figuring out interest rates, measuring the length of time required to complete a project, and determining the length traveled by an object.

Long division is also used in algebra to factor polynomials and solve equations. It is an essential tool for solving intricate challenges that consist of enormous values and requires accurate calculations.

Steps Involved in Long Division

Here are the steps involved in long division:

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

Step 2: Figure out how many times the divisor can be divided into the first digit or set of digits of the dividend. Write the quotient (the result of the division) above the digit or set of digits.

Step 3: Multiply the quotient by the divisor and note down the outcome 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: Bring down the following digit or set of digits from the dividend and append it to the remainder.

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

Examples of Long Division

Here are few 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







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

Example 3: Divide 3475 by 83.




83 | 3475







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

Common Mistakes in Long Division

Long division can be a problematic theory to conquer, and there are numerous common mistakes that students make when working with long division. One general error is to forget to write down the remainder when dividing. One more usual mistake is to incorrectly position the decimal point while dividing decimal numbers. Learners might also forget to carry over values while subtracting the product within the dividend.

To avoid making these mistakes, it is crucial to exercise long division frequently and pay close attention to ever stage of the procedure. It can further be helpful to revise your work using a calculator or by performing the division in reverse to assure that your solution is right.

In addition, it is essential to comprehend the fundamental principles regarding long division, such as the connection among the dividend, divisor, quotient, and remainder. By conquering the basics of long division and preventing usual mistakes, everyone can enhance their abilities and gain confidence in their skill to figure out intricate challenges.


Finally, long division is a crucial math idea which is important for working out complicated problems in several fields. It is used in finance, engineering, science, and math, making it a crucial skill for working professionals and learners alike. By mastering the procedure consisted in long division and understanding how to apply them to real-life challenges, everyone can obtain a deeper understanding of the complex workings of the world surrounding us.

If you need guidance understanding long division or any other arithmetic concept, Grade Potential Tutoring is here to help. Our expert teachers are available remotely or in-person to provide personalized and effective tutoring services to guide you succeed. Our teachers can guide you through the steps of long division and other mathematical ideas, support you figure out complicated problems, and offer the tools you require to excel in your studies. Contact us today to plan a tutoring class and take your math skills to the next stage.