May 04, 2023

Long Division - Steps, Examples

Long division is a crucial mathematical theory that has many real-world applications in different fields. One of its main uses is in finance, where it is utilized to calculate interest rates and find out loan payments. It is further used to work out taxes, investments, and budgeting, making it an essential skill for everyone working in finance.

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

Long division is further crucial in science, where it is applied to determine measurements and carry out scientific calculations. For example, astronomers use long division to calculate the distances between stars, and physicists use it to calculate the velocity of objects.

In algebra, long division is applied to factor polynomials and solve equations. It is a crucial tool for working out complex problems that consist of large numbers and need accurate calculations. It is also applied in calculus to figure out integrals and derivatives.

As a whole, long division is an important math concept that has many real-world applications in various fields. It is a fundamental arithmetic function that is used to work out complex challenges and is an important skill for anyone keen in science, finance, engineering, or math.

Why is Long Division Important?

Long division is a crucial mathematical theory that has several applications in various domains, including engineering, science and finance. It is an essential arithmetic operation which is used to figure out a wide spectrum of problems, for example, working out interest rates, determining the amount of time required to complete a project, and figuring out the length traveled by an object.

Long division is further utilized in algebra to factor polynomials and solve equations. It is a crucial tool for figuring out complex problems that involve large numbers and need precise calculations.

Stages Involved in Long Division

Here are the stages 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. Write 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 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







So, 562 divided by 4 is 140 with a remainder of 2.

Example 2: Divide 1789 by 21.




21 | 1789







So, 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 theory to master, and there are many common mistakes which learners make when performing long division. One common mistake is to forget to write down the remainder when dividing. Another common error is to incorrectly put the decimal point when dividing decimal numbers. Students may further forget to carry over figures when subtracting the product within the dividend.

To avoid making these mistakes, it is important to practice long division frequently and ready carefully ever step of the process. It can further be helpful to revisit your calculations using a calculator or by working the division in reverse to assure that your result is correct.

Furthermore, it is essential to understand the rudimental principles about long division, for instance, the relationship among the dividend, divisor, quotient, and remainder. By conquering the essentials of long division and preventing usual errors, anyone can enhance their abilities and gain confidence in their skill to figure out complex problems.


Finally, long division is a crucial math concept that is crucial for figuring out complicated challenges in several domains. It is applied in science, finance, engineering, and math, making it a crucial ability for professionals and learners alike. By mastering the stages involved in long division and understanding how to utilize them to practical problems, individuals can gain a detailed grasp of the complex workings of the world around us.

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