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What is Divisor?
A divisor is a number that divides another number either completely or with a remainder.
A divisor is represented in a division equation as:
Dividend ÷ Divisor = Quotient. |
On dividing 20 by 4 , we get 5. Here 4 is the number that divides 20 completely into 5 parts and is known as the divisor. Its division equation is
Similarly, if we divide 20 by 5, we get 4. Thus, both 4 and 5 are divisors of 20.
Divisor and factors
The divisor is any number that divides another number. A factor, however, is a divisor that divides the number entirely and leaves no remainder. So, all factors of a number are its divisors. But not all divisors will be factors.
In the example above, 4 and 5 are the factors of 20. Whereas, if we divide 20 by 3, it will not completely divide 20. Thus, 3 is not a factor of 20.
Let’s consider another example, 15 divided by 5 gives 3. Here, 5 is a divisor. Also, on dividing 15 divided by 3, we get 5. Here, 3 is a divisor.
The factors and divisors of 15 are: 1, 3, 5, 15
Finding factors of a number
To find the factors of a number, say 12, we follow the given steps:
1. Start with 1, and write multiplication facts such that the product is 12 such as 1 × 12.
2. Continue the same way to find other multiplication facts till we reach a pair of nearest factors or divisors as given:
1 ×12 , 2×6, 3×4
3. Write down all the numbers in the multiplication fact as these are the divisors of 12.
4. So, the divisors or factors of the number 12 are 1,2,3,4,6 and 12.
Different ways of representation of divisor
There are different styles of expressing a division equation. In the images below, the various methods of writing a divisor are shown below:
Special cases
1. The number 1 is the divisor of all the numbers.
Reason: When the divisor is 1, then the quotient is the same as the dividend.
Look at the given examples,
34 1 = 34
15 1 = 15
2. The number itself is always one of the divisors of the number.
Reason: When the divisor is the same as the dividend, then the answer to such a division is always 1.
Look at the given examples,
34 34 = 1
15 15 = 1
3. When the divisor is a smaller number than the dividend, then the answer is not a whole number but a decimal number.
For example, 510 = 0.5
Fun FactsIf we double the divisor, the quotient will be half. |
Frequently Asked Questions
- What is the difference between divisor and dividend?
- When we divide two numbers, the number that is being divided is the dividend, whereas the number by which we divide is the divisor. For example, 12 candies are to be divided among 3 children. So we have 12 ÷ 3. Here, 12 is the dividend, and 3 is the divisor.
- How is the divisor different from the factor?
- A divisor is any number that divides another number. A factor, however, is a divisor that divides the number entirely and leaves no remainder.
- Can a number be a divisor of itself?
- Yes, all numbers are divisors of themselves. This is because every number divides itself and gives 1 as the quotient. For example, if we have 12 ÷ 12, then 12 becomes the divisor of 12, and 1 becomes the quotient.
- What is the formula to find a divisor?
- If the remainder is 0, then Divisor = Dividend ÷ Quotient. If the remainder is not 0, then Divisor = (Dividend – Remainder) /Quotient.
Division Formula
The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are (÷) and (/). Thus, “p divided by q” can be written as: (p÷q) or (p/q). Let us see the division formula along with solved examples in the following section.
What Is Division Formula?
The division formula is the formula of division, which is one of the four basic operations of arithmetic. The division formula is used to equally split the number into many parts. Division Formula of a given value can be expressed as,
Where,
- The dividend is the number that is to be divided
- The divisor is the number to be divided with
- The quotient is the result.
Division Formula For Verification
Let us find out how we can verify our answer of division while using the division formula. For example, 8 ÷ 2 = 4, remainder = 0. In other words, 8=2×4+0. This method of verification can be expressed as:
Dividend = (Divisor × Quotient) + Remainder.
Let us consider one more example where the
- dividend = 9
- divisor = 3
- quotient = 3
- remainder = 0
Substituting the value in the formula, we get 9 = (3×3)+0=9. Therefore, our answer is correct.
Examples on Division Formula
Example 1: Divide, by using the division formula, the value of 500 by 50. What will be the quotient?
Solution:
To find: The quotient
Dividend = 500.
Divisor = 50.
Using Division Formula,
Dividend / Divisor = Quotient
(500/50) = 10
= 10
Answer: After the division, the quotient will be 10.
Example 2: 200 chocolates were distributed equally among 40 children. How many chocolates were given to each child? Calculate this by using the division formula.
Solution:
To find: Number of chocolates were given to each child.
Given information are:
Total chocolates = 200.
Total children = 40.
Using Division Formula,
Chocolates given to each child = (Total chocolates / Total Children)
= (200/40)
= 5
Answer: 5 chocolates were given to each child.
Example 3: Liza has 4 puppies. He bought 36 chewable bones to feed them equally. How many bones will each puppy get?
Solution:
The number of Puppies Liza has = 4.
The number of bones = 36.
Number of bones for each puppy = 36/4 = 9.
Answer: Each puppy will get 9 bones.
FAQs on Division Formula
What Are the Parts of Division Formula?
Here are the terms related to the division which are also considered as the parts of the division formula.
- Dividend
- Divisor
- Quotient
- Remainder
What Is Division Formula for Verification?
For rechecking our division answer we tend to follow a division method of verification. This method of verification can be expressed as Dividend = (Divisor × Quotient) + Remainder.
How To Use the Division Formula?
Generally, the division formula is used for splitting a number into equal parts. Let us consider an example.
Example: Sushi has 28 cookies and wishes to distribute them among her two kids equally. How will she divide the cookies equally?
Solution: Number of cookies = 28
Number of kids = 2
Number of cookies each kid will have = 28/2 = 14
Division Formula
Concept of Division
There are four basic operations of mathematics, which are Addition, Subtraction, Multiplication, and Division. The division is the process of breaking a number up into an equal number of parts. The division is an arithmetic operation used in Maths. It splits the number of items into different groups.
For example, 20 divided by 4: If we take 20 apples and put them into four equal-sized groups, there will be 5 apples in each group.
Method of Division
The mathematical expression 3 × 5 represents three groups with five items in each group. To get the product, students can build a model of three groups with five items in each group. We can also use repeated addition to find the product. They can add 3 five times like: 3 + 3 + 3 + 3 + 3 = 15.
It must be noted that multiplication will undo the division and vice versa. In other words, since 3×5=15,then15÷5=3.
Since division and multiplication are inverse operations of each other. Then students can use models similar to the models used in multiplication, to divide. In the expression 15÷3, you begin with fifteen items and want to know how many groups you can make with three items in each group. The answer, or quotient, is the number of groups. Let us look at an example.
15÷3=5
As we know that multiplication is a form of repeated addition. Similarly, the division is a form of repeated subtraction. For example, 15÷3 asks you to repeatedly subtract 3 from 15 until you reach zero:
- 15 – 3 = 12
- 12 – 3 = 9
- 9 – 3 = 6
- 6 – 3 = 3
- 3 – 3 = 0.
This process required 3 to be subtracted 5 consecutive times, so again we see that
15÷3=5.
The number which is divided is the dividend. And the number in which the dividend is being divided is the divisor. The answer to a division problem is the quotient. Example signs for “a divided by b”:
- a÷b &
- ^{a}/_{b}
So the Division formula is:
- Dividend÷Divisor=Quotient OR
- ^{Dividend}/_{Divisor}=Quotient
Special Cases
During the Division, some special cases are:
- Dividing by 1: When any number is divided by 1, then the answer remains the same. Thus, if the divisor is 1 then the quotient equals the dividend.
- Dividing by 0: No number can be divided by zero. Its answer is undefined.
- Dividend equals Divisor: If the dividend and the divisor both are the same number, but not zero, then the answer will always be 1.
Solved Examples for Division Formula
Q.1: Solve 221÷13.
Solution:
Here, Dividend = 221
Divisor = 13
Then, applying the simple division method we will get the quotient.
Therefore 221÷13=17
Division in Maths
There are four mathematical operations in Maths namely, Addition, Subtraction, multiplication, and Division. Division in Maths is considered as the most difficult among the four basic mathematical operations. The division is a method of splitting a number into an equal number of parts. For example, 20 ÷ 4, it states that 20 apples are split into 4 equal groups which further implies that 5 apples are there in one group. The diagram given below shows that there are 20 apples which are divided into 4 equal groups and each group has 5 apples.
In this article, we will discuss, division in maths, division formulas, division symbols, division examples, division rules etc.
Division Symbol
There are various division symbols that are used to represent division. The most commonly used division symbol is ÷, but sometimes the backslash / is also used to represent the division in the form of a fraction, where a Numerator value is written on the top and Denominator value on the bottom.
Example
“p divided by q”:
p÷q
Or
p/q
Dividend, Divisor, Quotient and Remainder Mean in Division in Maths.
When any number is divided by another number, we get the terms namely dividend, divisor, quotient and remainder.
- The dividend is defined as the number to be divided by another number.
- The divisor is a number that divides another number without leaving any remainder.
- The quotient is the result which is obtained after division.
- The remainder is the number that is left after division.
The above concept can be clearly understood through the image given below:
The division formula is :
Division Formula
In the above division formula,
- The dividend is the number to be divided by another number.
- The divisor is a number that divides another number without leaving any remainder.
- The quotient is the result which is obtained after division.
- The remainder is the number that is left after division.
Division Rules
Some of the division rules are given below:
- When the digit 0 is divided by another number, the result obtained is always 0. For example, 0 ÷ 3 = 3. This sentence means that 0 chocolates is distributed among 3 girls.
- When any number is divided by 0, it means that we are not dividing the number at all. For example, 3 ÷ 0 = is not possible in Mathematics. This sentence means that we have 3 chocolates but no girls to distribute the chocolates because we cannot divide any number by 0.
- When any number is divided by 1, we always get the same number. For example, 3 ÷ 1 = 3. This sentence means that 3 chocolates are distributed among 3 girls. Each girl received 1 chocolate.
- When any number is divided by the same number, we always get the number as 1. For example, 3 ÷ 3 = 1.
- Numbers should always be divided in the precise order. For example, 15 ÷ 3 = 5 and 3 ÷ 15 = 0.2 are two different cases. 15 chocolate divided by 3 girls is different from 3 sweets divided by 15 girls.
The fractions such as ½, ⅓, 1/4 etc are considered as division sums. For example, 1/3 is 1÷3. It means one chocolate divided by 3 girls.
Division Examples
Some of the division examples are given below:
1. Find the value of 60000 ÷ (- 10).
Solution:
60000 ÷ (-10)
= (60000 ) / (-10)
= (-60000) /(10)
= – 6000
2. Find the quotient value of 516 ÷ 12.
Solution:
Hence, the quotient value of 516 12 = 43
Solved Example
Some of the division examples with its solutions are given below:
1. Find the value of (-15625) ÷ (-125).
Solution:
(-15625) ÷ (-125)
= (-15625) / (-125)
= 15625/125
= 125
2. Divide -112 by -14.
Solution:
-112 ÷ (-14)
= (-112) /(-14)
= 112 / 14
= 8
3. Divide and find the quotient value of (-1728) ÷ 12.
Solution:
Hence, the quotient value of 1728 ÷ 12 = 144
Quiz Time
1. If 6 girls share 145 chocolates equally, how many sweets will be left?
- 24
- 0
- 6
- 1
2. (25 ÷ 5) ÷ ( 6-1)
- 5
- 1
- 625
- 25
3. What is the value of 323 ÷ 1
- 323
- 1
- 0
- Cannot find the answer
FAQs (Frequently Asked Questions)
- Example Simple Division and Long Division.
Ans. Simple Division – The simple division in Maths is a method used to divide small numbers into equal groups or parts. Simple division sums help in dividing easier and simple division questions into divisible terms. The simple division example is given below:
Long Division – The long division in Maths is a method used to divide larger numbers into small equal groups or parts. It helps in splitting the long division sums into a sequence of straightforward and easy steps. In long division, a larger number which is known as the dividend is divided by another number known as divisor which obtains the results quotient. The number which is left after division is known as the remainder. The long division example is given below:
- Explain the Relationship Between Multiplication and Division?
Ans. Multiplication and division are both closely related to each other. The division is basically an inverse process of multiplication. The division is a method of splitting a number into an equal number of parts while multiplication joins equal groups. For example,
3 × 5 = 15 , its inverse relation( in the division form will be the following)
15 ÷ 5 = 3
15 ÷ 3 = 5
Similarly, if we divide 40 ÷ 4 = 10, its inverse relation (in the multiplication form will be the following)
4 * 10 = 40
10 * 4 = 40
In the above example, we can see there are three numbers. It is because when we multiply two numbers ( which are known as factors), the result we get is called a product of two numbers whereas if we divide two numbers we get the factors as a result.
Divide
There’s no DIVIDE function in Excel. Simply use the forward slash (/) to divide numbers in Excel.
1. The formula below divides numbers in a cell. Use the forward slash (/) as the division operator. Don’t forget, always start a formula with an equal sign (=).
8a. First, divide the value in cell A1 by the value in cell A8. Fix the reference to cell A8 by placing a $ symbol in front of the column letter and row number ($A$8).
Explanation: when we drag the formula down, the absolute reference ($A$8) stays the same, while the relative reference (A1) changes to A2, A3, A4, etc.
If you’re not a formula hero, use Paste Special to divide in Excel without using formulas!
9. For example, select cell C1.
10. Right click, and then click Copy (or press CTRL + c).
11. Select the range A1:A6.
12. Right click, and then click Paste Special.
13. Click Divide.
14. Click OK.
Note: to divide numbers in one column by numbers in another column, at step 9, simply select a range instead of a cell.
Introduction to Divide in Excel
In excel, we can see that arithmetical operation has been used in various reports like inventory, monthly sales, salary, wages, etc… to calculate a simple addition, multiplication, division. The word division means the operation, which is the opposite of multiplication where the symbol of division can be a forward slash, or a line or a division sign, and this is also called a fraction. Each division equation has a name that we normally call a dividend, the divisor, and the quotient. These arithmetical operators work simply as a calculator wherein in excel; we need to use “equal” = sign in each cell to get the output.
The number which is divided is called the dividend, and the same number which the dividend is divided by is called the divisor. The output is normally called a quotient.
Division in Excel used in the same manner by using the “equal” sign in each cell to get the quotient as the output.
Divide Formula in Excel
How to Use Divide Formula in Excel?
Division operator can be used in excel by using the arithmetic operator slash (/) forward slash.
For example, click on the cell A2 with the mouse pointer and enter = sign and type the division sign (/) forward slash as =B2/C2 and press the enter key, where b is the dividend and c is the divisor which will give you the desired output.
For example, if you type =20/5, excel will give the output as 4. Make sure that you have to use an equal (=) sign in each cell to get the output. Otherwise, Excel will interpret and gives the output as a date.
Example #1
How to divide two columns in excel?
In this example, we will see step by step how the division (/) forward slash operator works in excel with the following steps.
Consider the below example, which has two columns, A and B, with specific numbers.
We will use the / forward slash operator to find the output.
- Click on the cell D3 column.
- Enter = (equal) sign
- Enter the formula by using the / forward slash operator.
- Enter =B3/C3 as shown below.
We will get the output as 5.
Drag the formula for the entire corresponding cell so that we will get the output as follows.
Example #2
How to use the division (/) operator with other Subtraction operators (-) in Excel?
In this example, we are going to see how to do multiple divisions step by step. Assume that we have multiple columns where we need to find out the Growth percentage of the sales. In this scenario, we can use nested division to fetch the exact output.
Consider the below example; we can see that month-wise quantity break up has been given for sales, and we have to calculate the growth percentage using the division operator.
We will see step by step how we got the growth percentage for individual salespersons.
- Click on the column Growth.
- Enter = equal sign in E3.
- Update the formula as =(D3-C3)/D3.
We will get the output as 8%.
Drag the formula for all the cells from top to bottom, and we will get the below result as follows.
The above sales result shows the growth of salespersons for the specific month. In this way, we can use them.
Example #3
How to Use Nested Parenthesis in Division Operator Using Addition (+)?
In this example, we are going to see how to use nested division by the following below steps as follows.
Consider the below example, which shows sales data month wise plus we have predicted future sales figures for Jan-19.
Now we are going to see how to use nested parenthesis in the division operator by following the below steps.
- Create a new column name Output.
- Click on the cell F2.
- Enter open parenthesis as shown below =(C2+D2)/E2.
- In this example, we have used opening and closing parenthesis by using both addition and division operator.
- We have added Nov-18 and Dec-18 months and divided the value with Jan-19 months to get the output.
- Convert the value to % as shown below.
Drag the formula for all the cells. Hence we will get the result as shown below.
Example #4
In this example, we will see how to find out the average of the student’s marks by using the division operator.
Let’s consider the below example where students scored marks for maths and science subjects, here we need to find out the average of student scored for both.
In this case, we can use the division operator to find out the average by following the below steps.
In order to calculate the average, a basic formula is the Total number of marks scored / Number of students.
- Create a new column as average.
- Enter the open parenthesis bracket as shown =(C2+E2)/2.
- We have added maths subject plus science subject divided by total subject.
We will get the output as 84.
Drag the formula for all the cells so that we will get the average of all students as the output shown below.
Example #5
Using IFERROR in a division operator
This example shows how to use division operation with the IFERROR condition to avoid #DIV/0! Error.
Mostly excel will throw an error if a cell has a blank value while using the division operator, as shown below.
In order to avoid this error, we will use the “IFERROR” condition so that we can overcome with these errors.
- Click on the cell name Result.
- Enter the IFERROR formula as shown below.
We will get the output as 4.
- =IFERROR(E2/F2,””) – which indicates we have used dividend number 20 /divisor number 5, which will give us the output of 5, and at last, we have closed the quotation marks to avoid DIV error.
- Drag the formula for all the cells.
- We will get the below output as follows.
Things to Remember about the Divide in Excel
- When using the Division operator, make sure that all cells have exact values. If the cell values are blank, excel will throw an #DIV Error.
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