May 04, 2023

Long Division - Steps, Examples

Long division is an important mathematical theory which has multiple practical utilizations in various domains. One of its main application is in finance, where it is utilized to calculate interest rates and find out loan payments. It is also utilized to work out taxes, investments, and budgeting, making it a crucial skill for anybody working in finance.

In engineering, long division is used to solve intricate challenges related to construction, design, and development. Engineers employ long division to calculate the weight which structures can bear, evaluate the toughness of materials, and plan mechanical networks. It is also used in electrical engineering to calculate circuit parameters and design complicated circuits.

Long division is further crucial in science, where it is used to calculate dimensions and carry out scientific workings. For instance, astronomers apply long division to calculate the length between stars, and physicists employ it to calculate the velocity of objects.

In algebra, long division is used to factor polynomials and solve equations. It is an important tool for working out complicated problems which include huge values and need precise calculations. It is further utilized in calculus to calculate derivatives and integrals.

As a whole, long division is an important mathematical concept that has many real-world utilizations in many domains. It is a fundamental mathematical function which is used to figure out complex problems and is an essential skill for anyone interested in engineering, science, finance, or math.

Why is Long Division Important?

Long division is an important mathematical theory which has numerous utilization in various fields, consisting of science, finance, engineering. It is an important math function which is utilized to figure out a wide range of problems, such as figuring out interest rates, measuring the length of time required to complete a project, and determining the length traveled by an object.

Long division is further applied in algebra to factor polynomials and work out equations. It is a crucial tool for working out complex challenges which involve large numbers and need accurate calculations.

Procedures Involved in Long Division

Here are the steps involved in long division:

Step 1: Note the dividend (the value being divided) on the left and the divisor (the number dividing the dividend) on the left.

Step 2: Determine how many times the divisor could be divided into the first digit or set of digits of the dividend. Write 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 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 handful of examples of long division:

Example 1: Divide 562 by 4.




4 | 562







As a result, 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







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

Common Mistakes in Long Division

Long division can be a problematic concept to conquer, and there are numerous general errors that students make when working with long division. One general error is to forget to write down the remainder when dividing. One more common error is to wrongly place the decimal point while dividing decimal numbers. Learners may also forget to carry over values while subtracting the product from the dividend.

To circumvent making these errors, it is essential to exercise long division daily and pay close attention to ever step of the procedure. It can also be beneficial to revisit your calculations utilizing a calculator or by performing the division in reverse to make sure that your answer is right.

In addition, it is crucial to comprehend the rudimental principles about long division, for instance, the relationship between the quotient, dividend, divisor, and remainder. By mastering the basics of long division and avoiding common errors, individuals can enhance their skills and gain confidence in their skill to figure out complicated challenges.


In conclusion, long division is a crucial math concept that is important for figuring out complex problems in many domains. It is used in finance, engineering, science, and math, making it a crucial ability for professionals and learners alike. By conquering the stages consisted in long division and comprehending how to utilize them to real-world problems, anyone can obtain a detailed comprehension of the complex workings of the world surrounding us.

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