May 04, 2023

Long Division - Steps, Examples

Long division is an important mathematical theory which has several real-life applications in different domains. One of its main uses is in finance, where it is utilized to calculate interest rates and determine loan payments. It is further utilized to work out budgeting, taxes, and investments, making it an essential skill for everyone working in finance.

In engineering, long division is utilized to solve complex challenges linked to development, construction, and design. Engineers employ long division to estimate the loads that structures can hold, determine the toughness of materials, and design mechanical systems. It is also used in electrical engineering to figure out circuit parameters and design complex circuits.

Long division is further essential in science, where it is used to determine measurements and execute scientific workings. For example, astronomers utilize long division to calculate the distances between stars, and physicists utilize it to determine the velocity of objects.

In algebra, long division is used to factor polynomials and solve equations. It is an essential tool for working out complicated challenges which include large numbers and need precise calculations. It is further used in calculus to figure out derivatives and integrals.

In conclusion, long division is an important math concept that has many practical utilizations in many domains. It is an essential math operation that is used to solve complicated problems and is an essential skill for anyone interested in finance, engineering, science, or math.

Why is Long Division Important?

Long division is an essential mathematical idea which has many applications in various fields, consisting of science, finance, engineering. It is an important mathematics function that is used to solve a broad range of challenges, such as working out interest rates, measuring the amount of time needed to finish a project, and figuring out the distance traveled by an object.

Long division is also used in algebra to factor polynomials and solve equations. It is a crucial tool for working out complicated problems which include large numbers 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 value 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. 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 write the outcome beneath 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. Write the remainder (the value left over 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 unless 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







Thus, 1789 divided by 21 is 85 with a remainder of 11.

Example 3: Divide 3475 by 83.




83 | 3475







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

Common Mistakes in Long Division

Long division can be a difficult theory to master, and there are many ordinary errors that learners make when performing long division. One usual mistake is to forget to write down the remainder when dividing. Another common error is to incorrectly position the decimal point while dividing decimal numbers. Students may further forget to carry over numbers while subtracting the product from the dividend.

To avoid making these errors, it is essential to work on long division regularly and be mindful of each step of the process. It can also be beneficial 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 comprehend the rudimental principles about long division, for example, the connection between the dividend, divisor, quotient, and remainder. By mastering the essentials of long division and preventing common errors, everyone can better their skills and obtain self-esteem in their ability to solve complicated problems.


Finally, long division is a crucial mathematical idea which is crucial for figuring out complex problems in many fields. It is applied in science, finance, engineering, and mathematics, making it an essential ability for professionals and learners alike. By mastering the steps involved in long division and comprehending how to utilize them to real-world challenges, individuals can obtain a deeper understanding of the complicated workings of the world surrounding us.

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