May 04, 2023

Long Division - Steps, Examples

Long division is an important math concept which has multiple real-life applications in different domains. One of its primary uses is in finance, where it is used to figure out interest rates and work out loan payments. It is further applied to figure out investments, budgeting, and taxes, making it a crucial skill for anybody engaged in finance.

In engineering, long division is applied to solve complex challenges related to development, construction, and design. Engineers utilize long division to calculate the loads that structures can endure, assess the toughness of materials, and plan mechanical systems. It is further used in electrical engineering to calculate circuit parameters and design complicated circuits.

Long division is further important in science, where it is applied to figure out measurements and execute scientific workings. For instance, astronomers apply long division to determine the length between stars, and physicists use it to figure out the velocity of objects.

In algebra, long division is used to factor polynomials and solve equations. It is an important tool for working out complex challenges that involve huge numbers and need accurate calculations. It is further used in calculus to work out derivatives and integrals.

In conclusion, long division is a crucial mathematical concept which has many real-world applications in many domains. It is a fundamental mathematical function that is used to work out complicated challenges and is an important skill for anyone interested in science, finance, engineering, or math.

Why is Long Division Important?

Long division is an important math theory which has several applications in different domains, involving engineering, science and finance. It is an important mathematics operation that is used to figure out a wide range of problems, such as calculating interest rates, determining the length of time needed to complete a project, and figuring out the length traveled by an object.

Long division is further utilized in algebra to factor polynomials and figure out equations. It is an important tool for solving complicated problems that consist of huge values and need precise calculations.

Stages Involved in Long Division

Here are the steps involved in long division:

Step 1: Write the dividend (the value 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. 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 write 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. Note down the remainder (the amount 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 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







So, 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







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

Common Mistakes in Long Division

Long division can be a difficult idea to conquer, and there are numerous ordinary errors that learners make when performing long division. One usual error is to forget to note down the remainder when dividing. Another common mistake is to incorrectly position the decimal point while dividing decimal numbers. Students might further forget to carry over figures while subtracting the product within the dividend.

To avoid making these errors, it is essential to exercise long division daily and ready carefully each stage of the procedure. It can also be helpful to check your work utilizing a calculator or by working the division in reverse to make sure that your answer is correct.

Furthermore, it is important to understand the rudimental principles about long division, for instance, the relationship among the divisor, quotient, dividend, and remainder. By conquering the essentials of long division and preventing usual mistakes, anyone can enhance their skills and gather confidence in their skill to figure out complicated challenges.


Finally, long division is an essential math idea that is crucial for working out complicated challenges in several domains. It is applied in science, finance, engineering, and mathematics, making it an important skill for working professionals and students alike. By conquering the procedure involved in long division and understanding how to apply them to real-life challenges, everyone can get a detailed comprehension of the complicated workings of the world surrounding us.

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