May 04, 2023

Long Division - Steps, Examples

Long division is an essential mathematical concept which has multiple real-world utilizations in different domains. One of its main uses is in finance, where it is used to calculate interest rates and work out loan payments. It is further applied to work out taxes, investments, and budgeting, making it a crucial skill for everyone involved in finance.

In engineering, long division is used to solve intricate challenges related to design, development, and construction. Engineers utilize long division to calculate the loads that structures can endure, assess the toughness of materials, and plan mechanical networks. It is also utilized in electrical engineering to figure out circuit parameters and design intricate circuits.

Long division is further essential in science, where it is utilized to figure out measurements and execute scientific calculations. For example, astronomers apply long division to calculate the distances between stars, and physicists employ it to determine the velocity of objects.

In algebra, long division is utilized to factor polynomials and solve equations. It is an essential tool for working out complicated challenges that consist of large numbers and need precise calculations. It is also utilized in calculus to work out derivatives and integrals.

As a whole, long division is a crucial mathematical concept that has many real-life uses in various domains. It is a rudimental arithmetic operation which is utilized to work out complex problems and is an essential skill for everyone keen in engineering, science, finance, or math.

Why is Long Division Important?

Long division is an important mathematical theory that has several applications in various fields, consisting of engineering, science and finance. It is an essential math function that is applied to figure out a wide spectrum of problems, for instance, working out interest rates, measuring the length of time required to complete a project, and determining the length traveled by an object.

Long division is further applied in algebra to factor polynomials and work out equations. It is a crucial tool for working out intricate problems that involve large numbers and need exact 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 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. Write 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 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 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: Replicate steps 2 to 5 until 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







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







So, 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 many common errors which students make when performing long division. One usual mistake is to forget to write down the remainder when dividing. Another common mistake is to incorrectly position the decimal point while dividing decimal numbers. Students might also forget to carry over figures when subtracting the product within the dividend.

To avoid making these errors, it is crucial to practice long division frequently and be mindful of ever step of the procedure. It can further be helpful to check your work utilizing a calculator or by performing the division in reverse to make sure that your answer is correct.

Additionally, it is crucial to get a grasp of the rudimental principles regarding long division, such as the link among the dividend, divisor, quotient, and remainder. By conquering the essentials of long division and avoiding common mistakes, everyone can enhance their abilities and gain confidence in their skill to solve complicated challenges.


Finally, long division is an essential mathematical idea which is essential for figuring out complex challenges in many domains. It is applied in finance, engineering, science, and mathematics, making it an important skill for working professionals and students alike. By mastering the stages consisted in long division and getting a grasp of how to use them to practical problems, individuals can obtain a detailed grasp of the complex functions of the world surrounding us.

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