May 04, 2023

Long Division - Steps, Examples

Long division is an important mathematical concept which has many practical uses in various domains. One of its primary application is in finance, where it is applied to figure out interest rates and work out loan payments. It is further applied to calculate taxes, investments, and budgeting, making it an essential skill for anybody involved in finance.

In engineering, long division is utilized to solve complicated challenges linked to development, construction, and design. Engineers use long division to calculate the loads that structures can hold, assess the strength of materials, and plan mechanical networks. It is also applied in electrical engineering to determine circuit parameters and design complex circuits.

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

In algebra, long division is applied to factor polynomials and solve equations. It is an important tool for figuring out complex challenges that consist of huge numbers and need accurate calculations. It is further utilized in calculus to calculate integrals and derivatives.

As a whole, long division is a crucial math concept which has several real-world applications in many domains. It is a fundamental math function which is utilized to solve complicated problems and is a crucial skill for anyone keen in science, finance, engineering, or arithmetic.

Why is Long Division Important?

Long division is an essential math concept which has many uses in distinguished fields, involving engineering, science and finance. It is a fundamental mathematics function that is applied to work out a broad array of problems, such as figuring out interest rates, determining the amount of time needed to complete a project, and figuring out the distance traveled by an object.

Long division is further utilized in algebra to factor polynomials and solve equations. It is an essential tool for figuring out intricate challenges which involve large numbers and requires precise calculations.

Procedures Involved in Long Division

Here are the procedures 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: Determine 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) above 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. Note down 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 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







Therefore, 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







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

Common Mistakes in Long Division

Long division can be a problematic idea to master, and there are many common mistakes that learners make when working with long division. One general mistake is to forget to note down the remainder when dividing. Another common mistake is to incorrectly place the decimal point while dividing decimal numbers. Students may also forget to carry over numbers while subtracting the product from the dividend.

To circumvent making these errors, it is important to work on long division daily and pay close attention to ever stage of the process. It can also be helpful to revisit your work 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 basic principles about long division, such as the link among the quotient, dividend, divisor, and remainder. By conquering the fundamentals of long division and preventing usual mistakes, individuals can better their skills and gather self-esteem in their skill to figure out complex challenges.


Ultimately, long division is a crucial math concept that is essential for solving complex problems in various domains. It is utilized in finance, engineering, science, and mathematics, making it an essential skill for working professionals and students alike. By mastering the steps consisted in long division and comprehending how to use them to real-life challenges, anyone can gain a detailed grasp of the complex workings of the world around us.

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