May 04, 2023

Long Division - Steps, Examples

Long division is an important mathematical idea that has several practical utilizations in various domains. One of its main uses 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 an essential skill for anyone involved in finance.

In engineering, long division is utilized to solve complicated challenges linked to construction, design, and development. Engineers use long division to calculate the weight that structures can endure, evaluate the toughness of materials, and design mechanical systems. It is further used in electrical engineering to determine circuit parameters and design intricate circuits.

Long division is further essential in science, where it is utilized to figure out measurements and carry out scientific calculations. For instance, astronomers apply long division to determine the distances between stars, and physicists employ it to calculate the velocity of objects.

In algebra, long division is utilized to factor polynomials and solve equations. It is an essential tool for working out complicated challenges which involve huge values and requires precise calculations. It is also applied in calculus to work out integrals and derivatives.

Overall, long division is an essential math concept that has multiple practical uses in many fields. It is an essential mathematical operation which is applied to work out complex problems and is an important skill for anyone interested in finance, engineering, science, or math.

Why is Long Division Important?

Long division is an important mathematical theory that has several utilization in distinguished fields, including finance, engineering, and science. It is an important mathematics function that is utilized to figure out a broad spectrum of challenges, such as calculating interest rates, measuring the length of time needed to complete a project, and figuring out the distance traveled by an object.

Long division is also applied in algebra to factor polynomials and figure out equations. It is a crucial tool for working out complicated challenges which include large numbers and need precise calculations.

Stages Involved in Long Division

Here are the stages involved in long division:

Step 1: Note the dividend (the value being divided) on the left and the divisor (the value 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. 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 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 following digit or set of digits from the dividend and append it to the remainder.

Step 6: Repeat 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







As a result, 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







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

Common Mistakes in Long Division

Long division can be a challenging concept to master, and there are many ordinary errors which students make when working with long division. One general error is to forget to write down the remainder when dividing. Another usual error is to incorrectly position the decimal point when dividing decimal numbers. Learners may further forget to carry over numbers while subtracting the product from the dividend.

To prevent making these mistakes, it is important to practice long division regularly and ready carefully each stage of the procedure. It can further be beneficial to check your calculations using a calculator or by working the division in reverse to assure that your answer is right.

In addition, it is essential to understand the fundamental principles behind long division, such as the connection between the dividend, divisor, quotient, and remainder. By mastering the fundamentals of long division and avoiding common mistakes, anyone can improve their abilities and obtain self-esteem in their skill to solve complicated challenges.


Finally, long division is a crucial math concept which is important for solving complex problems in several domains. It is used in science, finance, engineering, and mathematics, making it an important ability for professionals and learners alike. By mastering the stages involved in long division and understanding how to use them to real-world problems, individuals can get a detailed grasp of the complex workings of the world surrounding us.

If you require guidance comprehending long division or any other arithmetic concept, Grade Potential Tutoring is here to help. Our adept tutors are accessible online or in-person to provide customized and effective tutoring services to help you be successful. Our tutors can assist you through the steps of long division and other math ideas, assist you work out complex problems, and offer the tools you require to excel in your studies. Reach us today to schedule a tutoring lesson and take your math skills to the next stage.