May 04, 2023

Long Division - Steps, Examples

Long division is an essential math idea which has multiple real-world utilizations in various fields. One of its main uses is in finance, where it is applied to calculate interest rates and determine loan payments. It is further utilized to figure out investments, budgeting, and taxes, making it an important skill for everyone involved in finance.

In engineering, long division is applied to solve complicated problems in connection to design, development, and construction. Engineers employ long division to estimate the loads that structures can bear, determine the strength of materials, and design mechanical systems. It is further applied in electrical engineering to figure out circuit parameters and design complicated circuits.

Long division is also essential in science, where it is used to figure out dimensions and carry out scientific calculations. For instance, astronomers utilize long division to determine the length between stars, and physicists employ 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 working out complex challenges which involve huge values and need precise calculations. It is also used in calculus to calculate derivatives and integrals.

As a whole, long division is an essential mathematical concept that has multiple practical utilizations in many domains. It is a fundamental math operation that is applied to solve complex challenges and is an important skill for anyone interested in finance, engineering, science, or math.

Why is Long Division Important?

Long division is an important math theory which has numerous utilization in distinguished domains, including engineering, science and finance. It is an important arithmetic function that is utilized to solve a broad range of challenges, for instance, calculating interest rates, measuring the amount of time required to finish a project, and figuring out the distance traveled by an object.

Long division is further used in algebra to factor polynomials and work out equations. It is a crucial tool for figuring out complicated challenges that consist of large values and need accurate calculations.

Stages 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: Figure out 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 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. Write the remainder (the amount left over 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: Replicate steps 2 to 5 unless all the digits in the dividend have been refined.

Examples of Long Division

Here are some examples of long division:

Example 1: Divide 562 by 4.




4 | 562







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

Example 2: Divide 1789 by 21.




21 | 1789







Therefore, 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 concept to master, and there are many ordinary mistakes that students make when performing long division. One usual 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 might also forget to carry over numbers when subtracting the product from the dividend.

To circumvent making these mistakes, it is important to work on long division daily and be mindful of ever stage of the process. It can further be helpful to revise your work using a calculator or by working the division in reverse to make sure that your result is right.

Additionally, it is important to understand the rudimental principles behind long division, for example, the link between the divisor, quotient, dividend, and remainder. By conquering the fundamentals of long division and avoiding usual mistakes, everyone can improve their skills and gain self-esteem in their ability to work out intricate challenges.


In conclusion, long division is an essential math concept which is crucial for solving complex problems in various fields. It is used in engineering, science, finance, and mathematics, making it an important ability for professionals and students alike. By conquering the stages involved in long division and comprehending how to apply them to real-life challenges, individuals can obtain a detailed grasp of the complex functions of the world surrounding us.

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