May 04, 2023

Long Division - Steps, Examples

Long division is an important mathematical concept which has several real-world uses in various domains. One of its main application is in finance, where it is used to calculate interest rates and determine loan payments. It is further applied to calculate 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 employ long division to calculate the loads which structures can endure, evaluate the toughness of materials, and plan mechanical systems. It is also used in electrical engineering to determine circuit parameters and design complicated circuits.

Long division is further crucial in science, where it is used to determine measurements and execute scientific calculations. Such as astronomers use long division to calculate the length between stars, and physicists utilize 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 which involve huge numbers and need accurate calculations. It is further used in calculus to work out integrals and derivatives.

As a whole, long division is an essential math concept which has multiple real-world utilizations in several fields. It is a rudimental arithmetic function that is utilized to figure out complicated problems and is an important skill for anyone keen in engineering, science, finance, or math.

Why is Long Division Important?

Long division is an essential mathematical idea that has several uses in various fields, involving finance, engineering, and science. It is a fundamental math function which is used to solve a broad range of problems, for example, calculating interest rates, measuring the amount of time required to finish a project, and finding the distance traveled by an object.

Long division is further applied in algebra to factor polynomials and work out equations. It is a crucial tool for figuring out complicated problems that consist of enormous values and requires accurate calculations.

Procedures Involved in Long Division

Here are the steps 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. Write 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 outcome 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. Note down the remainder (the value remaining 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: Repeat 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







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

Example 2: Divide 1789 by 21.




21 | 1789







So, 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 challenging idea to conquer, and there are several ordinary errors that learners make when performing long division. One common mistake is to forget to write down the remainder when dividing. Another usual mistake is to wrongly place the decimal point when dividing decimal numbers. Students may also forget to carry over numbers while subtracting the product within the dividend.

To avoid making these mistakes, it is crucial to work on long division frequently and be mindful of each 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 result is right.

Furthermore, it is crucial to get a grasp of the fundamental principles about long division, for instance, the link between the divisor, quotient, dividend, and remainder. By mastering the fundamentals of long division and preventing usual mistakes, individuals can enhance their abilities and obtain self-esteem in their skill to solve complicated challenges.


In conclusion, long division is a crucial mathematical concept which is crucial for working out complex problems in various fields. It is utilized in engineering, science, finance, and mathematics, making it an important ability for professionals and students alike. By conquering the stages involved in long division and comprehending how to utilize them to real-life challenges, anyone can gain a detailed understanding of the complex workings of the world around us.

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