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Addition, subtraction, multiplication, and division are the four fundamental operations in mathematics. The division of numbers into equal parts is known as division. Dividend, divisor, remainder, and quotient are the four essential components of the division process. The divisor is the number that divides another number, while the dividend is the number that is being divided. A quotient is a result obtained through division, whereas the remainder is the amount of the dividend remaining after division. We need to study more about the division process. In this article, we will look at the divisor, one of the most important components of division in detail.
Read Also: Divisibility by 9 and 3
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Key Terms - Divisor, division, dividend, formula, factors, symbol, number, divisor formula.
Division and Symbol
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The function of the division is to divide the given into an equal number of parts. They help us to divide a particular number into smaller ones equally.
For Instance,
Example. Rema has 50 mangoes and she needs to divide those mangoes equally among her 2 children. How does she divide?
Ans. Total number of mangoes - 50
Number of children in which mango to be divided- 2
50 ÷ 2 = 25
Hence the 2 children will get 25 mangoes each
Usually, the symbol used for division is [ ÷ ], or else the two numbers will be divided using a [/] symbol, here the numerator will be written above and the denominator will be written below.
Check Important Notes for Divisibility Rules
Formula of Division
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Dividend ÷ Divisor = Quotient
As previously discussed, during the division process, we will be given a specific number to divide. This number is known as a dividend, and the number by which the dividend must be divided is known as the divisor. The final result of this division process is called the quotient. The divisor was not able to dive a particular number and this number is called the remainder.
Formula of Divisor
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The basic formula for division: Dividend ÷ Divisor = Quotient
This can be also written as Divisor = Dividend ÷ Quotient
In some cases, we separate dividend and divisor with[/] symbol instead of [÷], it will turn out as Dividend/Divisor = Quotient
Let us look into the examples
- 40÷2 = 20, here in this example 40 is the dividend,2 is the divisor and 20 is the quotient
- 65÷5 = 30, here in this example 65 is the dividend, 5 is the divisor, 30 is the quotient
- 33÷3 =11, here in this example 33 is the dividend. 3 is the divisor, 11 is the quotient
- 7÷2 = 3.5, here in this example 7 is the dividend, 2 is the divisor, 3.5 is the quotient. 7 is divided by 2 and the result is a fraction of 3.5
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Representation of Divisor
Let us look into a pictorial representation to get a better understanding of the divisor. The below picture shows the dividend and divisor separately.
How to find a Divisor?
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You can easily identify a divisor from a particular division problem, as we know the division is an important part of the division process.
Let's take a look at an example.
20÷4=5 The dividend is 20, the divisor is 4, and the quotient is 5. In the division process, the divisor is used to divide a specific number; in this case, the number 4 is divided by the number 20, resulting in the number 5.
Also Check:
Factors of a Number
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As we have studied in our primary classes, factors are figures that divide a specific number accurately in half. They are also called divisors. The term divisor refers to a number that splits the dividend. A divisor is also known as a factor of a number when it divides the dividend fully and leaves no remainder. Thus, all divisors are factors of a number, but not all divisors must be factors of a number. Let us look into the divisors of 12, 24, 16 to get a better understanding.
Divisors of 12
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1×12 =12
2×6 =12
3×4 =12
The factors of the number 12 are 1, 2, 3,4,6 and 12
Therefore, the number of divisors of 12 is 6, they are 1,2,3,4,6,12
Also Read More:
Divisors of 24
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1×24 = 24
12×2 = 24
6×4 = 24
8×3 = 24
The factors of the number 24 are 1,2,3,4,6,8,12,24
Therefore the number of divisors of 24 is 8, they are 1,2,3,4,6,12,24
Divisors of 16
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1×16 =16
8×2 =16
4×4 =16
The factors of the number 16 are 1,2,4,8,16
Therefore the divisors of 16 are 1, 2,4,8,16
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Things to Remember
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- Divisor is the number by which the dividend must be divided.
- A divisor will not be zero, if a particular number got divided by zero the result will be undefined. If we divide the dividend zero with a divisor, the quotient will always be zero.
- The function of a divisor is to divide a particular number into parts
- Even if the quotient and divisor are switched, a division problem remains true.
- When we divide a divisor fully the remainder will be turned out as zero and also if we divide a divisor partially the remainder will be turned out as a non-zero number
- A positive or negative number can be used as a divisor.
Check More: Rationalize the Denominator
Sample Questions
Ques. What do you mean by Divisor? (3 marks)
Ans. In division, a number by which the dividend must be divided is known as the divisor. The divisor is the number that divides the dividend, and the dividend is the number that is divided.
Dividend÷DIvisor=Quotient
Ques. How can we identify the divisor from a fraction number? (3 marks)
Ans. The fraction number will always be in the p/q form. According to the conditions of the division process, the numerator is the dividend and the denominator is the divisor
For example,
Consider the number 24/2
Here 24 is the dividend and 2 is the divisor
Ques. What are the most important characteristics of a divisor? (5 marks)
Ans. A divisor cannot be zero; therefore, if a number is divided by zero, the result is undefined. The quotient will always be zero if we divide the dividend zero by a divisor. A divisor's job is to divide a large number into smaller ones. Even A division problem still exists if the quotient and divisor are switched. When we divide a divisor completely, the remainder will be zero, and when we divide a divisor partially, the remainder will be a non-zero number. A divisor can be either a positive or negative number.
Ques. Explain the place of remainder in the division? (3 marks)
Ans. A division is made up of the remainder. The remainder is the numeric value that is received as a result of division. After certain steps in the case of an incomplete division, we get a remainder. When a few numbers are split into groups with an equal number of things, the remainder is left over.
Ques. What are the characteristics of a remainder? (5 marks)
Ans. The remainder has the following characteristics:
The divisor will always exceed the remainder in every division. When the remainder of a division is larger than or equal to the divisor, the division has been performed incorrectly. The quotient can be greater, smaller, or equal to a reminder of a given division. When a division is finished or the divisor divides the dividend completely, the remainder is 0.
Ques. What is the general form of a division? (5 marks)
Ans. One of the four basic mathematical operations is division. The process of division is also known as repetitive subtraction. A mathematical symbol represents division. A simple horizontal line with a dot above and below it makes up the symbol. The quotient, dividend, divisor, and remainder are all required in the general division formula. One of the division methods that is used to divide two numbers is the long division method.
Ques. What do you mean by the Long Division Method? (5 marks)
Ans. This method is used to solve division problems. The divisor is written outside the right parenthesis in the long division method. The quotient is placed outside the overbar, on top of the dividend's place, and the dividend is placed inside it. The result of a dividend divided by any divisor is known as a quotient in mathematics. The quotient is the number of times the divisor appears in the dividend without leaving a negative remainder.
Ques. What is the Distinction Between a Dividend and a Divisor? (3 marks)
Ans. A divisor is a device that divides a number into groups of equal size. The dividend is the amount that is being divided, and the divisor is the amount that divides it.
For instance
Consider the number 30/2
Here 30 is the dividend and 2 is the divisor
Ques. How do you find the greatest common divisor? (5 marks)
Ans. The greatest positive number that is a common divisor for a given set of positive numbers is referred to as the Greatest Common Divisor (GCD). It's also called the Greatest Common Factor (GCF) or the Highest Common Factor (HCF) (GCF). Let's see what the greatest common divisor of 10 and 22 is. The divisors of 10 and 22 will be listed. The divisors of 10 are 1, 2, 5, and 10. 22 has divisors of 1, 2, 11, and 22. 10 and 22 have the same common divisor: 1, 2. The GCD = 2
Ques. What is the difference between a factor and a divisor? (3 marks)
Ans. The term divisor refers to a number that splits the dividend. A divisor is also known as a factor of a number when it divides the dividend entirely and leaves no remainder. Thus, all divisors are factors of a number, but not all divisors must be factors of a number.
For instance, The factors of the number 12 are 1, 2, 3,4,6 and 12
Therefore, the number of divisors of 12 are 1,2,3,4,6,12.
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