May 04, 2023

Long Division - Steps, Examples

Long division is an essential math idea which has many practical uses in various fields. One of its primary application is in finance, where it is applied to calculate interest rates and determine loan payments. It is further utilized to calculate taxes, investments, and budgeting, making it a crucial skill for anybody involved in finance.

In engineering, long division is used to solve intricate problems related to development, construction, and design. Engineers utilize long division to calculate the loads which structures can endure, determine the strength of materials, and design mechanical systems. It is further utilized in electrical engineering to determine circuit parameters and design intricate circuits.

Long division is further essential in science, where it is applied to calculate measurements and execute scientific workings. Such as astronomers apply long division to figure out the distances between stars, and physicists utilize it to determine the velocity of objects.

In algebra, long division is used to factor polynomials and solve equations. It is a crucial tool for solving complex challenges that include large values and requires accurate calculations. It is also utilized in calculus to work out derivatives and integrals.

Overall, long division is an important mathematical concept that has several real-world uses in several domains. It is an essential math operation that is applied to figure out complex challenges and is a crucial skill for everyone keen in finance, engineering, science, or arithmetic.

Why is Long Division Important?

Long division is an essential math idea that has many utilization in distinguished fields, including engineering, science and finance. It is a fundamental math function which is applied to work out a wide range of problems, for instance, calculating interest rates, measuring the length of time needed to finish a project, and finding the length traveled by an object.

Long division is also applied in algebra to factor polynomials and figure out equations. It is a crucial tool for figuring out intricate challenges which include huge values and requires precise calculations.

Procedures Involved in Long Division

Here are the stages 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: Figure out how many times the divisor could be divided into the first digit or set of digits of the dividend. Write the quotient (the result of the division) prior the digit or set of digits.

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

Step 4: Subtract the result achieved in step 3 from the digit or set of digits in the dividend. Note down the remainder (the amount remaining after the division) underneath the subtraction.

Step 5: Bring down the next 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 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







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

Common Mistakes in Long Division

Long division can be a difficult concept to conquer, and there are several common errors that students make when working with long division. One common mistake is to forget to write down the remainder when dividing. One more common mistake is to wrongly put the decimal point while dividing decimal numbers. Students may further forget to carry over figures while subtracting the product within the dividend.

To circumvent making these mistakes, it is crucial to practice long division daily and ready carefully ever stage of the process. It can further be beneficial to check your calculations using a calculator or by working the division in reverse to make sure that your answer is right.

Furthermore, it is important to comprehend the rudimental principles about long division, for example, the relationship between the divisor, quotient, dividend, and remainder. By mastering the basics of long division and avoiding common mistakes, individuals can enhance their abilities and gain confidence in their ability to figure out complicated challenges.


Ultimately, long division is a crucial mathematical theory that is essential for working out complex problems in various fields. It is used in science, finance, engineering, and mathematics, making it a crucial skill for professionals and learners alike. By conquering the stages involved in long division and getting a grasp of how to apply them to real-world challenges, individuals can get a detailed grasp of the complex functions of the world around us.

If you want guidance understanding long division or any other arithmetic idea, Grade Potential Tutoring is here to assist you. Our expert tutors are accessible online or in-person to offer personalized and productive tutoring services to support you be successful. Our tutors can guide you with the stages in long division and other arithmetic concepts, support you work out complicated problems, and provide the tools you want to excel in your studies. Call us today to schedule a tutoring lesson and take your math skills to the next stage.