May 04, 2023

Long Division - Steps, Examples

Long division is an essential math concept that has multiple practical utilizations 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 work out budgeting, taxes, and investments, making it an important skill for anybody working in finance.

In engineering, long division is utilized to figure out complex challenges related to development, construction, and design. Engineers use long division to calculate the weight that structures can endure, assess the strength of materials, and design mechanical systems. It is further utilized in electrical engineering to figure out circuit parameters and design complicated circuits.

Long division is further crucial in science, where it is utilized to calculate dimensions and carry out scientific workings. For example, astronomers utilize long division to determine the length between stars, and physicists utilize 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 complicated challenges which include large numbers and requires precise calculations. It is further applied in calculus to calculate integrals and derivatives.

As a whole, long division is a crucial math concept that has multiple real-world utilizations in several fields. It is an essential arithmetic operation which is applied to solve complex challenges and is a crucial skill for anyone keen in finance, engineering, science, or mathematics.

Why is Long Division Important?

Long division is an important math concept that has many uses in various domains, consisting of science, finance, engineering. It is a fundamental arithmetic function which is used to solve a broad range of challenges, for example, working out interest rates, determining the length of time needed to complete a project, and figuring out the length traveled by an object.

Long division is also applied in algebra to factor polynomials and figure out equations. It is a crucial tool for figuring out intricate problems that include huge values and need accurate 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) 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 obtained in step 3 from the digit or set of digits in the dividend. Write the remainder (the amount 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: Replicate steps 2 to 5 until all the digits in the dividend have been refined.

Examples of Long Division

Here are handful of 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







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 difficult idea to master, and there are several common errors that learners make when performing long division. One general error is to forget to note down the remainder when dividing. Another common mistake is to incorrectly put the decimal point while dividing decimal numbers. Learners 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 frequently and ready carefully ever step of the process. It can also be helpful to check your work using a calculator or by working the division in reverse to ensure that your result is right.

In addition, it is essential to understand the fundamental principles behind long division, for instance, the relationship among the quotient, dividend, divisor, and remainder. By mastering the essentials of long division and preventing usual errors, individuals can better their skills and gather self-esteem in their ability to figure out intricate challenges.


Ultimately, long division is an essential math theory that is crucial for solving complex problems in many fields. It is used in finance, engineering, science, and mathematics, making it a crucial ability for professionals and students alike. By conquering the steps consisted in long division and comprehending how to utilize them to real-world challenges, anyone can obtain a detailed comprehension of the complicated functions of the world surrounding us.

If you require guidance comprehending long division or any other mathematical theory, Grade Potential Tutoring is here to assist you. Our experienced tutors are available online or face-to-face to give customized and productive tutoring services to support you succeed. Our tutors can assist you with the steps of long division and other math concepts, support you solve complex challenges, and provide the tools you want to excel in your studies. Contact us today to plan a tutoring class and take your math skills to the next level.