Long Division – Definition with Examples

Definition of Long Division

In Math, long division is the mathematical method for dividing large numbers into smaller groups or parts. It helps to break down a problem into simple and easy steps. The long divisions have dividends, divisors, quotients, and remainders. In a long division problem, the dividend is the large number that is divided by another number called the divisor. The quotient is the result of the division, and the excess quantity that cannot be divided is called the remainder

Example of Long Division 

Here is an example that will help us understand this concept:

Example of Long Division

As 75 is not a multiple of 4, it is not divisible by 4 and will leave a remainder at the end. 

Symbol of Division

To show that two numbers are divided, we can add a division sign ‘÷’ between them. So, for example, if we have to show 36 divided by 6, we can write it as 36 ÷ 6. 

We can also show it in a fraction form as 366. 

Steps to Carry Out Long Division

There are five steps to solve every long division problem with ease. 

Steps to Carry Out Long Division

Let’s have a look at the examples given below for a better understanding of the concept.

Better Understanding of long division

Dividing Decimals Using A Long Division

Long division can also be used to divide decimal numbers into equal groups. It follows the same steps as that of long division, namely, – divide, multiply, subtract, bring down and repeat or find the remainder. 

Here’s an example of long division with decimals.

Dividing Decimals Using A Long Division

Fun Facts About Long Division

  • If the dividend is 0, the quotient will always be zero.
  • The remainder is always less than the dividend.
  • Multiplying the quotient with the divisor and adding the remainder will give the dividend. 

(Divisor x Quotient) + Remainder = Dividend 

  • When the remainder is 0, the dividend is the product of divisor and quotient.

Divisor x Quotient = Dividend, when remainder = 0

Conclusion

Long Division is an instrument that allows you to divide large numbers into multiple smaller groups or parts. When we divide a dividend with a divisor, the quotient obtained is the number of groups that can be made, and the remainder identifies how many elements or numbers that will be left ungrouped. To understand this concept even better, check out the wide range of interesting exercises available on SplashLearn and become a long division wiz! 

Solved Examples 

Question 1:  Divide 726 by 4 

Ans: 

Divide 726 by 4

Hence, the quotient of the problem is 181, and the remainder is 2.

Question 2: What is the remainder when we divide 248 by 8?

Ans: 

Divide 248 by 8

Hence, the quotient of the problem is 31, and the remainder is 0. 

Question 3: Laila’s mother collected all family pictures and wanted to place all of them in an album. If each page of an album can contain 9 pictures, how many pages of the album will she need if there are 285 pictures?

Ans:

Divide 285 by 9

The quotient of the problem is 31, and the remainder is 6. So, she needs 31 + 1 (for the remaining six pictures) or 32 pages. 

Practice Problems

Long Division

Attend this Quiz & Test your knowledge.

1

On dividing 426 by 4, we get the remainder as

0
2
4
6
CorrectIncorrect
Correct answer is: 2
On dividing 426 by 4, we will get the quotient as 106 and remainder as 2.
2

Find the dividend if the divisor is 8, quotient is 71 and remainder is 4.

562
560
576
572
CorrectIncorrect
Correct answer is: 572
Dividend = (Divisor x Quotient) + Remainder = (8 x 71) + 4 = 572
3

Find the digit that can replace A in the following division problem.

Long Division – Definition with Examples
3
4
5
6
CorrectIncorrect
Correct answer is: 6
A × 5 = 30. So, A must be 30 ÷ 5 or 6.

Frequently Asked Questions

No, division by 0 is not defined in Math generally.

In Math, long division is the mathematical method for dividing large numbers into multiple smaller groups or parts. The number which we divide into small groups is called the dividend, the number by which we divide is called the divisor. It helps to break down a problem into simple and easy steps. 

​​We can verify the quotient and the remainder of the division using the division formula: (Divisor x Quotient) + Remainder = Dividend 

The short division is great for dividing larger numbers by one-digit numbers, whereas the long division is handy for dividing large numbers by numbers with two or more digits.