May 04, 2023

Long Division - Steps, Examples

Long division is a crucial math concept which has several practical utilizations in different domains. One of its main application is in finance, where it is applied to calculate interest rates and determine loan payments. It is also applied to figure out taxes, investments, and budgeting, making it a crucial skill for everyone working in finance.

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

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

In algebra, long division is applied to factor polynomials and solve equations. It is an essential tool for figuring out complex challenges that involve large values and need accurate calculations. It is also used in calculus to calculate integrals and derivatives.

Overall, long division is an essential mathematical theory that has several practical uses in various fields. It is an essential mathematical operation which is used to work out complicated challenges and is a crucial skill for everyone interested in engineering, science, finance, or math.

Why is Long Division Important?

Long division is an important math idea that has several applications in various domains, including engineering, science and finance. It is an essential math operation that is applied to solve a broad array of challenges, such as figuring out interest rates, measuring the amount of time needed to complete a project, and finding the distance traveled by an object.

Long division is further applied in algebra to factor polynomials and figure out equations. It is a crucial tool for solving complex problems which involve enormous numbers and requires precise calculations.

Stages Involved in Long Division

Here are the procedures involved in long division:

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







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 concept to conquer, and there are several general errors that learners make when working with long division. One general error is to forget to write down the remainder when dividing. One more usual error is to wrongly put the decimal point while dividing decimal numbers. Students may also forget to carry over values when subtracting the product within the dividend.

To circumvent making these errors, it is essential to work on long division frequently and ready carefully each step of the process. It can further be helpful to revisit your calculations utilizing a calculator or by performing the division in reverse to ensure that your result is right.

In addition, it is important to get a grasp of the basic principles regarding long division, for example, the connection among the dividend, divisor, quotient, and remainder. By conquering the basics of long division and avoiding usual mistakes, individuals can enhance their abilities and gather confidence in their skill to figure out complex problems.


In conclusion, long division is a crucial mathematical idea that is essential for working out complex problems in many domains. It is used in engineering, science, finance, and math, making it an important ability for working professionals and students alike. By mastering the stages involved in long division and comprehending how to utilize them to real-world challenges, everyone can obtain a detailed comprehension of the complex functions of the world surrounding us.

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