May 04, 2023

Long Division - Steps, Examples

Long division is a crucial mathematical concept that has several practical utilizations in different domains. One of its main uses is in finance, where it is applied to figure out interest rates and determine loan payments. It is further applied to figure out taxes, investments, and budgeting, making it a crucial skill for anybody working in finance.

In engineering, long division is utilized to figure out complicated challenges in connection to development, construction, and design. Engineers utilize long division to determine the loads that structures can bear, assess the strength of materials, and design mechanical systems. It is further utilized in electrical engineering to calculate circuit parameters and design complex circuits.

Long division is also crucial in science, where it is used to calculate measurements and perform scientific workings. For example, astronomers utilize long division to calculate the distances between stars, and physicists use it to calculate the velocity of objects.

In algebra, long division is used to factor polynomials and solve equations. It is an important tool for working out complex problems which consist of huge numbers and need precise calculations. It is further applied in calculus to figure out integrals and derivatives.

As a whole, long division is an essential math theory which has many practical utilizations in various fields. It is a rudimental arithmetic operation which is applied to work out complicated problems and is an important skill for everyone interested in engineering, science, finance, or mathematics.

Why is Long Division Important?

Long division is an important mathematical theory that has many utilization in various domains, including engineering, science and finance. It is a fundamental arithmetic operation which is used to work out a broad array of problems, for example, figuring out interest rates, determining the length of time required to finish a project, and figuring out the distance traveled by an object.

Long division is further used in algebra to factor polynomials and figure out equations. It is an essential tool for figuring out complicated challenges which consist of enormous values and requires accurate calculations.

Procedures 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: Determine how many times the divisor can be divided into the first digit or set of digits of the dividend. Note down the quotient (the result of the division) above the digit or set of digits.

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

Step 4: Subtract the outcome obtained in step 3 from the digit or set of digits in the dividend. Write the remainder (the value left over after the division) underneath 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 refined.

Examples of Long Division

Here are few examples of long division:

Example 1: Divide 562 by 4.




4 | 562







As a result, 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 challenging theory to conquer, and there are numerous general errors that students make when performing long division. One common mistake is to forget to write down the remainder when dividing. Another usual error is to wrongly place the decimal point when dividing decimal numbers. Learners might also forget to carry over values when subtracting the product within the dividend.

To prevent making these errors, it is important to exercise long division regularly and pay close attention to ever stage of the process. It can further be helpful to revisit your calculations using a calculator or by performing the division in reverse to make sure that your solution is right.

In addition, it is essential to get a grasp of the fundamental principles regarding long division, for example, the relationship between the quotient, dividend, divisor, and remainder. By conquering the basics of long division and preventing common errors, everyone can better their skills and gain self-esteem in their skill to solve complicated challenges.


Finally, long division is an essential math idea which is important for working out complicated challenges in many domains. It is used in science, finance, engineering, and mathematics, making it a crucial skill for professionals and learners alike. By mastering the stages involved in long division and getting a grasp of how to apply them to real-world problems, anyone can gain a deeper grasp of the complicated workings of the world around us.

If you require help understanding long division or any other arithmetic idea, Grade Potential Tutoring is here to help. Our experienced teachers are accessible online or face-to-face to give personalized and effective tutoring services to guide you succeed. Our teachers can assist you across the stages in long division and other arithmetic concepts, support you figure out complex challenges, and provide the tools you need to excel in your studies. Connect with us right now to schedule a tutoring class and take your math skills to the next level.