Open In App

Long Division Method

Improve
Improve
Like Article
Like
Save
Share
Report

Long Division is a technique of dividing numbers, algebraic expressions, and decimals stepwise and sequentially. In this technique the number which is to be divided is called Dividend, the number which divides is called Divisor, the number which we get as a result of division is called a Quotient, and the number which is left as extra on dividing is called Remainder. In this article, we will learn in detail about the long division method, the components of the long division method, the Division Algorithm, the division of numbers, decimals, and algebraic expression.

What is Long Division Method?

Long Division Method is a method of dividing large numbers, algebraic expressions, and decimals by breaking them into smaller numbers at every step. In this method, the dividend is subtracted by a number which is the multiple of the divisor nearest but less than the dividend. Long division method can be understood by repeated subtraction. In the repeated subtraction method we subtract the dividend by divisor until we get zero or a number less than the dividend.

Components of Long Division Method

There are four components of the long division method, these are dividend, divisor, quotient, and remainder.

  • Dividend: It is the number that is to be divided. It is the largest among all the four components.
  • Divisor: It is the number that divides the dividend. It is less than or equal to dividend.
  • Quotient: This is the number that gets as a result of dividing Dividend by Divisor. It can be greater than or less than or equal to the divisor.
  • Remainder: It is the number that we get as extra in the long division method. It is less than the divisor. If Remainder is zero then the dividend is multiple of divisor.

We can understand the components better from the image added below:

dividend, divisor, quotient, and remainder.

How to do Long Division?

Long Division Method is performed by subtracting the dividend by a multiple of the divisor which is either equal to or less than the dividend. Division is one of the four basic arithmetic operations used in a range of applications from daily life stuff to complex mathematical calculations. Let’s learn the steps involved in the Long Division Method.

Steps to Calculate Long Division

While performing the Long Division Method we need to follow the below-mentioned steps

Step 1: Observe the dividend digit by digit from the left-hand side and check if it is greater than or equal to the divisor. You should not consider the whole dividend for the division. You should consider the first one, two, or three digits of the dividend from Left Hand Side that should be at the maximum nearest 9th multiple of the divisor.

Step 2: Take the multiple of divisor which is equal to or nearest but less than the dividend. At this stage, the quotient should be not greater than 9.

Step 3: The multiple of the divisor is subtracted from the dividend. You will get the difference.

Step 4: Besides the difference that you got, bring down the next digit of the dividend and divide using step 2.

Step 5: Repeat the process until no digit of dividend is left and the remainder is either zero or less than the divisor.

Now we will use these steps in performing division and learn different cases of Divison.

Long Division Example

A solved Example of Long Division has been discussed below:

Example: Find the quotient and remainder when 12456 is divided by 24.

To find the quotient and remainder for dividend = 12456 and divisor = 24, we can perform long division as follows:

Long Division Example

Calculate Long Division of Numbers

In this case, we will learn to divide numbers into two categories. One is division with remainder and the other is division without remainder.

Long Division with Remainder

In this, we will learn about two cases:

Case 1: When the first digit of the dividend is greater than or equal to the divisor

Example: Find quotient and remainder when 341 is divided by 3.

Solution:

Step 1: Observe the dividend from Left Hand Side. We find that first digit is 3 which is equal to dividend.

Step 2: Write 1 in the Quotient column and write three below the first digit of dividend 342 as 3 is the multiple of 3 which is nearest to the first digit of the dividend which is also 3. Find the difference we get 3 – 3 = 0.

Step 3: In this step bring down the second digit of the dividend beside 0. Write 1 in quotient column as 3 is the multiple of 3 which is nearest to 4. Subtract 4 – 3 we get 1.

Step 4: In this step bring down the last digit 1 of the dividend beside the 1 that was left in step 4.

Step 5: Write 3 in the Quotient column as 9 is the multiplier of 3 which is nearest to 11. Subtract 11 – 9 we get 2. Now no digit of the remainder is left.

Long Division of 341 by 3

Hence, we find that on dividing 341 by 3 we get 113 as the quotient and 2 as the remainder.

Case 2: When the first digit of the dividend is less than the divisor

For Example, Divide 541 by 7.

Step 1: Observe that the first digit of dividend is 5 which is less than 7 hence we can not proceed division with the first digit. Thus we need to divide the first two digits of the dividend i.e. 54 by 7.

Step 2: Write 7 in the Quotient column as 49 is the multiple of 7 which is nearest to 54. Subtract 54 – 49 we get 5.

Step 3: Write the last digit 1 of the dividend beside 5 which is obtained in step 2.

Step 4: Divide 51 by 7. Write 7 in the quotient column because 49 is the multiple of 7 nearest to 51. Subtract 51 – 49, we get 2.

Division of 541 by 7

Hence, on dividing 541 by 7 we get 77 as quotient and 2 as remainder.

Long Division without Remainder

In this case, the steps are the same as Division with Remainder just only one difference that here remainder at the end of differentiation is zero.

Let us understand it with an example.

Example: Divide 436 by 4.

Solution:

Step 1: Observe that the first digit of dividend is equal to divisor i.e. both are 4 here.

Step 2: Write 1 in quotient column as 4 is the nearest multiple to itself. Subtract 4 – 4 we get zero.

Step 3: Write down the next digit of dividend i.e. 3 beside the zero obtained in step 2. We see that 3 is less than 4 which is the divisor hence we need to put 0 in the quotient.

Step 4: Write down the next digit of dividend i.e. 6 beside 3 obtained in the previous step. Now we have 36.

Step 5: Write 9 in the quotient column as 36 is the multiple of 4 which is nearest and equal to 36. Subtract 36 – 36, we get zero.

Long Divsion of 436 by 4

Hence on dividing 436 by 4, we get 109 as the quotient and 0 as the remainder.

Long Division by 2-Digit Number

In this, the steps and process followed are the same as that in one digit just in this case divisor is of two digits hence we have to see the first two digits of the dividend are greater, equal, or less than the divisor. Let’s understand with the help of an Example of Long Division

For Example, Divide 226 by 16

Step 1: Observe the first two digits of the dividend. Here it is 22 greater than divisor 16. Hence we can divide the first two digits. Note if the first two digits have been smaller then divide the three digits at a time.

Step 2: Since we have 22 as the first two digits of dividend, write 1 in the quotient column as 16 is the multiple of 16 which is nearest to 22. Subtract 22 – 16, we get 6.

Step 3: Write the last digit 6 of the dividend beside the 6 obtained in Step 2. Now we have to divide 66 by 16.

Step 4: Write 4 in the quotient column as 64 is the multiple of 16 nearest to 66. Subtract 66 – 64 we get 2 as the remainder.

Long Division of 226 by 16

Hence on dividing 226 by 16, we get 14 as quotient and 2 as remainder.

Note: For division without remainder all the steps will be the same but you will get the remainder zero in the final step. The same procedure is followed for three-digit, four-digit, etc. divisors with the basic difference that in the case of a three-digit divisor observe the first three digits of the dividend, four digits of the dividend for the four-digit divisor, and so on.

Long Division of Polynomials

In the long division of polynomials, observe the degree of dividend and the divisor and write the quotient in such a manner that the product of the quotient and divisor is the term equal to the first term of the dividend. The Long Division of Polynomial Let’s understand this in steps.

How to do Polynomial Long Division?

We can use the following steps to perform long division between polynomials:

Step 1: Arrange the indices of a polynomial in descending order i.e., variables with higher exponents are arranged first followed by variables with lower exponents. Replace missing terms with 0 as coefficient. Example: 3x2+0x+1, 4x3+3x2+x-4

Step 2: Divide the first term of the dividend by the first term in the divisor which gives the first term of the quotient.

Step 3: Perform multiplication between the divisor and the first term of the quotient.

Step 4: Subtract the result obtained in step-3 from the dividend and bring down the next term. This will be our new dividend.

Step 5: Repeat step-2 to step-4 to find the next term of the quotient.

This process is continued until we get the remainder. This may be zero or index less than the divisor.

Example of Polynomial Long Division

The above-mentioned steps of the Polynomial Long Division can be better understood with the help of an example.

Example: Divide 4x3+3x2+x-4 by x -2

Example of Polynomial Long Division

Learn More, Dividing Polynomials

Long Division with Decimal

The long division of decimals is done in a similar way as the long division of numbers with a reminder that when the decimal comes, put that decimal in the quotient at that time. Let’s learn how to divide a decimal by a whole number.

Division of Decimals by a Whole Number

Let’s understand how to divide a decimal by a whole number in a stepwise manner with the help of an example.

Let’s say we have to divide 21.6 by 2, then we can find the quotient and remainder using the following steps:

Step 1: We see that the first digit is similar to that of the divisor hence first divide 2 by 2. Here we write 1 as the quotient and the remainder will be zero at this step.

Step 2: Now write down the second digit 1 beside the 0 obtained in step 1. We see that 1 is less than 2 hence we can’t divide 1 by 2 therefore write 0 in the quotient.

Step 3: Before writing the third and last digit i.e. 6 from the dividend we see that there is a decimal. At this time place the decimal point in quotient.

Step 4: Now write down the third digit i.e. 6 beside 1 obtained in step 2. Now we have 16 which is to be divided by 2.

Step 5: Write 8 in the quotient and subtract 16 from 16 which gives the remainder zero.

Long Division of 21.6 by 2

Hence, we find that on dividing 21.6 by 2 we get 10.8 as the quotient and zero as the remainder.

Dividing a Number to Decimal Places

In this case, we try to divide a number to the required number of decimal places or till we get zero as the remainder. Let’s learn the steps of dividing a number to decimal places using examples

Example: Divide 18 by 4.

Solution:

Step 1: We see that first digit of the dividend i.e, 1 is less than 4 hence we try to divide two digits at a time.

Step 2: On dividing 18 by 4 write 4 as quotient because 16 is the multiple of 4 which is nearest to 18. Subtract 16 from 18 we get the remainder as 2. But we won’t stop here, we will try dividing it further.

Step 3: Place a decimal in the quotient and at the same time place a zero beside 2 which is the remainder. Now at this stage, we have 20 which is to be divided by 4.

Step 4: Write 5 in the quotient as a 20 is multiple of 4 and hence we get the remainder as zero.

Long division of 18 by 4 to one decimal place

Thus on dividing 18 by 4, we get 4.5 as the quotient and zero as the remainder.

Note: If the number doesn’t get divided completely at step 4 then again place a zero beside the remainder obtained in step 4 but don’t place a decimal point again in the quotient.

Long Division Application

Long Division Method has got its application in finding Highest Common Factor (HCF), Lowest Common Multiple, and Finding Square Root apart from solving basic arithmetic problems.

Highest Common Factor by Long Division Method

Highest Common Factor popularly called HCF is the largest factor of two given numbers. Highest Common Factor of two numbers can be find out using Long Division Method. Let’s understand through it an example

Example: Find the HCF of 16 and 24

HCF using Long Division Method

Lowest Common Multiple by Long Division Method

Lowest Common Multiple popularly called LCM is the lowest multiple of two numbers which is common to both Numbers. Let’s Understand it through an Example:

Example: Find the LCM of 16 and 24 using Long Division Method

LCM using Long Division Method

Square Root by Long Division Method

We can find the square root of a number using Long Division Method. Let’s learn using the following Example.

Example: Find the Square Root of 144

Square Root Using Long Division

Division by Repeated Subtraction

In division by repeated subtraction, the dividend is subtracted by the divisor and the difference of the previous step is subtracted by the divisor in the next step until we get zero or a number that is less than the divisor. The number of steps taken to get zero or the number less than the divisor is the quotient. Let’s understand it with examples

Example: Divide 16 by 4 using the Repeated Subtraction Method

Here we have 16 as dividend and 4 as the divisor.

Step 1: 16 – 4 = 12

Step 2: 12 – 4 = 8

Step 3: 8 – 4 = 4

Step 4: 4 – 4 = 0

Here we got zero in the fourth step. Hence on dividing 16 by 4, we get 4 as the quotient and 0 as the remainder.

Example: Divide 20 by 6 using the Repeated Subtraction Method

Step 1: 20 – 6 = 14

Step 2: 14 – 6 = 8

Step 3: 8 – 6 = 2

Now 2 can’t be subtracted from 6 hence we stop the process here. Thus on dividing 20 by 6, we get 3 as the quotient and 2 as the remainder.

Division Algorithm

Division Algorithm is a way of testing if your long division method is correct or not. Division Algorithm states that when the product of the divisor and quotient is added to the remainder, it gives the dividend.

Dividend = Divisor × Quotient + Remainder

For Example, if 75 is divided by 18, we will get the quotient as 4 and the remainder as 3. Now we can check it using division algorithm as follows:

Divisor = 18

Quotient = 4

Remainder = 3

Divisor × Quotient + Remainder = 18 × 4 + 3 = 75 = Dividend

Read More,

Long Division Problems

Some Long Division Questions have been discussed below with their detailed solution:

Problem 1: Solve by long division (6x2+7x-20)÷(2x+5)

Solution:

Long Division Example 1

Quotient=3x-4

Remainder=0

Problem 2: If 200 chocolates are distributed among 40 students. Find the number of chocolate each student get.

Solution:

If 200 chocolates are being distributed among 40 students, each student will receive equal amount of chocolates, which can be calculated as 200/4, 

Using long division, we get

Long Division Example 2

Thus, each student will get 5 chocolates.

Problem 3: If a train travels 180 km in 4hr, find the distance covered by the train in 1hr.

Solution:

If train travels 180 Km in 4 hours,

then in 1 hour train travels = 180/4 [Using Unitary Method]

Which can be calculated as follows:

Long Division Example 3

Thus, in one hour train travels 45 Km.

Problem 4: Find the quotient and remainder when 32.5 is divided by 5

Solution:

To find the qotient and remainder for dividend = 32.5 and divisor =5, we can perform long division as follows:

Long Division Example 4

Thus, Quotient = 6.5 and Remainder = 0.

Problem 5: Find the Square Root of 44100 using Long Division Method

Solution:

The square root of 44100 is 210. It can be calculated using Long Division Method as follows:

Square Root of 44100 using Long Division Method

FAQs on Long Division Method

Q1: What is Long Division Method?

Answer:

Long Division Method is a method of dividing number by subtracting a multiple of divisor which is nearest to the dividend. It is a step wise divison method.

Q2: How to do Long Division Method?

Answer:

Long Division Method is done by subtracting the multiple of divisor from the dividend at each step till we get a number that is less than divisor.

Q3: How to do Long Division in Step by Step manner?

Answer:

The steps of perfroming Long Division is mentioned below:

Step 1: Observe the dividend digit by digit from the left-hand side and check if it is greater than or equal to the divisor. You should not consider the whole dividend for division. You should consider the first one, two, or three digits of the dividend from Left Hand Side that should be at the maximum nearest 9th multiple of the divisor.

Step 2: Take the multiple of divisor which is equal to or nearest but less than the dividend. At this stage, the quotient should be not greater than 9.

Step 3: The multiple of the divisor is subtracted from the dividend. You will get the difference.

Step 4: Beside the difference that you got, bring down the next digit of the dividend and divide using step 2.

Step 5: Repeat the process until no digit of dividend is left and the remainder is either zero or less than the divisor.

Now we will use these steps in performing division and learn different types of Divison

Q4: What are the Components of Long Divison Method?

Answer:

There are four components of long division method, Dividend, Divisor, Quotient and Remainder

Q5: What is Division Algorithm?

Answer:

Division Algorithm states that, Dividend = Divisor ✕ Quotient + Remainder. It is a method to check if your division is correct or not.

Q6: What is Division by Repeated Subtraction?

Answer:

In division by repeated subtraction, the dividend is subracted by the divisor and the difference obtained is again subtracted by divisor till we get zero or a number less than divisor. The number steps involved is the quotient and the difference obtained in the last step in the remainder.



Last Updated : 29 Feb, 2024
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads