May 04, 2023

Long Division - Steps, Examples

Long division is an essential mathematical concept that has several real-life utilizations in various fields. One of its main application is in finance, where it is utilized to calculate interest rates and find out loan payments. It is further used to calculate taxes, investments, and budgeting, making it a crucial skill for anybody working in finance.

In engineering, long division is utilized to solve intricate problems in connection to construction, design, and development. Engineers utilize long division to determine the loads that structures can endure, evaluate the strength of materials, and design mechanical systems. It is also utilized in electrical engineering to figure out circuit parameters and design complex circuits.

Long division is further crucial in science, where it is utilized to figure out measurements and perform scientific calculations. For instance, astronomers utilize long division to calculate the length between stars, and physicists utilize it to determine the velocity of objects.

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

As a whole, long division is an essential math theory which has many real-world utilizations in several fields. It is a rudimental mathematical operation which is utilized to work out complex problems and is a crucial skill for everyone keen in science, finance, engineering, or mathematics.

Why is Long Division Important?

Long division is an essential mathematical theory which has many utilization in distinguished fields, consisting of engineering, science and finance. It is an essential arithmetic operation that is utilized to figure out a wide array of challenges, for example, figuring out interest rates, determining the length of time needed to complete a project, and determining the length traveled by an object.

Long division is also applied in algebra to factor polynomials and work out equations. It is an essential tool for figuring out complicated challenges which include large values and requires precise calculations.

Stages Involved in Long Division

Here are the stages involved in long division:

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

Step 2: Determine 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) prior 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 result achieved in step 3 from the digit or set of digits in the dividend. Write the remainder (the value left over after the division) below 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 some examples of long division:

Example 1: Divide 562 by 4.




4 | 562







So, 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







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

Common Mistakes in Long Division

Long division can be a problematic idea to master, and there are many ordinary errors that students make when performing long division. One usual error is to forget to note down the remainder when dividing. One more usual error is to incorrectly place the decimal point while dividing decimal numbers. Students might further forget to carry over figures while subtracting the product from the dividend.

To prevent making these errors, it is essential to practice long division regularly and be mindful of ever stage of the procedure. It can also be helpful to check your calculations utilizing a calculator or by performing the division in reverse to make sure that your solution is correct.

In addition, it is essential to get a grasp of the fundamental principles regarding long division, such as the relationship among the quotient, dividend, divisor, and remainder. By mastering the essentials of long division and preventing usual mistakes, anyone can improve their skills and gain self-esteem in their ability to figure out intricate problems.


Ultimately, long division is a fundamental math theory which is crucial for figuring out complex challenges in several domains. It is used in engineering, science, finance, and math, making it an important skill for professionals and learners alike. By conquering the procedure involved in long division and understanding how to utilize them to real-world challenges, individuals can get a deeper grasp of the complicated workings of the world surrounding us.

If you require assistance comprehending long division or any other arithmetic concept, Grade Potential Tutoring is here to assist you. Our experienced instructors are available online or face-to-face to give customized and productive tutoring services to support you be successful. Our teachers can assist you across the stages in long division and other mathematical theories, help you solve complex problems, and offer the tools you require to excel in your studies. Call us today to plan a tutoring session and take your math skills to the next stage.