May 04, 2023

Long Division - Steps, Examples

Long division is an important math theory which has multiple real-world utilizations in different domains. One of its primary application is in finance, where it is applied to figure out interest rates and find out loan payments. It is also used to work out taxes, investments, and budgeting, making it a crucial skill for anybody working in finance.

In engineering, long division is utilized to figure out complex problems related to development, construction, and design. Engineers employ long division to estimate the weight that structures can bear, assess the toughness of materials, and plan mechanical systems. It is further applied in electrical engineering to determine circuit parameters and design complicated circuits.

Long division is also essential in science, where it is utilized to calculate measurements and perform scientific calculations. For instance, astronomers utilize long division to calculate the length between stars, and physicists employ it to calculate the velocity of objects.

In algebra, long division is utilized to factor polynomials and solve equations. It is an important tool for figuring out complex problems which consist of huge values and requires precise calculations. It is further used in calculus to calculate derivatives and integrals.

Overall, long division is an essential math theory that has several real-world uses in various domains. It is a fundamental mathematical operation which is used to solve complicated problems and is an important skill for anyone interested in engineering, science, finance, or mathematics.

Why is Long Division Important?

Long division is an essential mathematical theory that has many uses in various domains, including engineering, science and finance. It is an important mathematics operation which is used to work out a wide range of problems, such as figuring out interest rates, determining the length of time required to finish a project, and finding the length traveled by an object.

Long division is further applied in algebra to factor polynomials and figure out equations. It is an essential tool for solving complicated challenges that consist of large values and requires accurate calculations.

Procedures Involved in Long Division

Here are the procedures 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 can be divided into the first digit or set of digits of the dividend. Note down the quotient (the result of the division) above the digit or set of digits.

Step 3: Multiply the quotient by the divisor and note down the result 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 following 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 processed.

Examples of Long Division

Here are few 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







As a result, 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 challenging theory to conquer, and there are several ordinary errors which learners make when working with long division. One common error is to forget to note down the remainder when dividing. One more common error is to incorrectly place the decimal point while dividing decimal numbers. Learners might also forget to carry over figures while subtracting the product from the dividend.

To circumvent making these errors, it is important to practice long division daily and be mindful of ever stage of the procedure. It can also be beneficial to check your calculations using a calculator or by working the division in reverse to ensure that your answer is right.

In addition, it is essential to get a grasp of the basic principles about long division, such as the connection between the quotient, dividend, divisor, and remainder. By mastering the essentials of long division and avoiding usual mistakes, anyone can improve their skills and obtain confidence in their ability to figure out complex challenges.


In conclusion, long division is a crucial math concept that is essential for solving complex challenges in several domains. It is used in finance, engineering, science, and math, making it a crucial skill for working professionals and learners alike. By mastering the procedure consisted in long division and getting a grasp of how to apply them to practical problems, everyone can get a detailed comprehension of the complex workings of the world around us.

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