An Introduction to Divisor
In Mathematics, the four fundamental operations widely used are Addition, Subtraction, Multiplication, and Division. The role of the division is to break the number into equal parts. The four terms used in the division to divide the number into equal parts are dividend, divisor, quotient, and remainder. The number which divides another number is termed as a divisor whereas the number which is being divided is termed as a dividend. A quotient is a result which we get in the process of division whereas the remainder is the portion of the dividend that is left after the division. In this article, we will study division meaning, divisor definition, divisor formula, divisor examples, etc.
Division Meaning
The Division is a basic Arithmetic operation used widely in Mathematics. Division breaks a number into an equal number of parts. It divides a given number of items into different groups.
For example, If you take 20 apples and place them into 4 equal-sized groups, there will be 5 apples in each group.
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Division Symbol
Although there are numerous division signs that people use, the most common division sign is ( ÷ ) and in case of fraction backlash (/) is used, where the numerator is written on the top and the denominator is written on the bottom.
Division example sign for x divided by z
x ÷ z
x/z
Division Formula
Dividend ÷ Divisor = Quotient
Or,
Quotient = Dividend/ Divisor
Divisor Meaning
In division, we divide a number by any other number to obtain another number as a result. The number which is getting divided is known as the dividend and the number which divides a given number is termed as the divisor. The number which we receive as a result is known as the quotient. The divisor which does not divide the given number completely is referred to as the remainder.
Divisor Definition
A Divisor is a Number that Divides the Other Number in the Calculation.
For example: when you divide 28 by 7, the number 7 will be considered as a divisor, as 7 is dividing the number 28 which is a dividend.
7) 28 (4
- 28
--------
0
--------
Divisor Formula
Operation division can be written in the following manner:
Quotient= Dividend ÷ Divisor
The above remainder equation can also be written in the following manner
Divisor = Dividend ÷ Quotient
Divisor Example
You can understand the divisor meaning in a better way by looking at divisor examples given below:
If 33 ÷ 11= 3, then 33 is the dividend and 11 is the divisor of 33 which divides the number 33 into 3 equal parts
If 50 ÷ 5 = 10, then 50 is the dividend and 5 is the divisor of 50 which divides the number 50 into 10 equal parts
1÷ 2 = Here divisor 2 is dividing the number 1 into a fraction.
5) 46 (9
- 45
--------
1
-------
In the above example - 5 is the divisor, 46 is the dividend, 9 is the quotient and 1 is the remainder.
General Form of Division
The division is one of the 4 primary mathematical operations. Division can also be called the process of repetitive subtraction. The division is denoted by a mathematical symbol. The symbol consists of a short horizontal line with a dot, above and below it. The general formula for the division requires the quotient, the dividend, the divisor, and the remainder. Long Division Method is one of the methods of division that is used to divide two given numbers. The general formula of division is:
Dividend = (Divisor × Quotient) + Remainder
Verification of division can also be done to check if the process done is right or not. Division can also be seen as the reverse of multiplication and the check by substituting the values in the General form of Division.
Special Cases of Division-
When any number is divided by 1, the quotient is always to equal the dividend and the answer will be the same as the dividend.
If the dividend is equal to the divisor, the same numbers (but not 0) then the answer will always be 1.
No number can ever be divided by 0. That's why when a number is divided by 0 the answer is always undefined.
Divisor in Division
In a division, the divisor is the number that divides another number. It might or might not leave a remainder. In other words, in a division with given numbers, the divisor divides the dividend into equal groups. The number getting divided in a division is called the dividend. Some properties of the divisor of a division are-
In any division, the remainder is always less than the divisor.
If the quotient is similar to the dividend, then number 1 will always be the divisor of all the numbers.
If the dividend and the divisor are equal in a situation, the quotient will always be 1.
If the remainder is 0, that implies that the divisor has divided the dividend, completely.
If in a division, the divisor is greater than the dividend, then the resultant number will always be a decimal number.
In a division, a quotient is a number that is obtained upon dividing a dividend by a divisor. When any number is left over after the division. That is called the remainder.
Remainder in Division
The remainder is a part of a division. Remainder is the left-over digit that is received while performing division. In case of an incomplete division after certain steps we get a remainder as a result. The remainder is left-over when a few numbers are divided into groups with an equal number of things.
Some properties of the remainder are -
In any division, the divisor will always be greater than the remainder. If the remainder of a given division is greater than or equal to the divisor, this indicates that the division is performed incorrectly.
A reminder of a given division can be either greater, smaller, or equal to the quotient.
When a division is complete or when the divisor completely divides the dividend, the remainder is always 0.
Solved Example
There are 26 men and Rs. 5876 is distributed equally among all men. How much money will each person receive?
Solution: Money received by 26 men = Rs. 5876
Money each person will receive = 5876 ÷ 26
Divisor = 26 , Dividend = 5876
Quotient = 22, Remainder =0
Therefore, each man will receive = Rs. 22
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If 9975 Kg of rice is packed in 95 jute bags, how much rice will each jute bag contain?
Solution: Quantity of rice packed in 95 jute bags = 9975 kg
Quantity of rice packed in 1 bag = 9975÷ 95
Divisor = 95 , Dividend = 9975
Quotient =105, Remainder = 0
Hence, the quantity of rice each bag will contain = 105 kg
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Interesting Facts
De Morgan in 1845 introduced the oblique bar used as a sign of that process in the division.
Division of a number by 0 is not defined
The term colon is used to represent the division in some non-English speaking countries. The colon was introduced by Gottfried Wilhelm Leibniz in his 1684 Acta eruditorum.
“÷” also known as obelus was introduced by Swiss Mathematician Johann Rahn in 1659.
Quiz Time
The given number that we are dividing by is called
Remainder
Divisor
Quotient
Dividend
456 ÷ 7
7
76
70
75
In a division sum, the dividend is 336, the quotient is 42 and the remainder is 0. What will be the divisor?
7
9
8
2
FAQs on Divisor
1. What are the Key Properties of the Divisor?
Some important properties of the divisor to remember are:-
Divisor divides the number into parts.
The Dividend can be completely or partially divided by the divisor. The remainder will be 0 if divided completely and the remainder will be non-integer if divided partially.
Divisors can be either positive or negative numbers.
The divisor 0 will obtain the result as 0, each time for any dividend.
Any number that divides an integer exactly, leaving without any remainder is also stated as the divisor.
The divisors 1 and -1 can divide every integer present in the number line.
2. Is 1 a Prime Divisor?
A prime number is a positive integer which retains exactly two factors, which means that it can be divided by only two numbers i.e. 1 and the number itself. For example-if p is a prime number, then its only two factors will necessarily be 1 and p itself.
Number 1 is not considered as a prime divisor as for the number to be considered as the prime divisor, it is necessary to have 2 factors. But number 1 is not meeting the condition. So, 1 is not considered as a prime divisor.
3. What is Multiplication?
Multiplication is a mathematical operation that is used to multiply different types of numbers and to get the desired product, which is the obtained result after multiplication. There are different terms that are used while performing the multiplication of numbers. They are-
Multiplicand- Multiplicand is the total number of items in each group.
Multiplier- Multiplier is the total number of equal groups.
Product- Product is the desired result after performing multiplication on numbers.
Multiplication symbol- Cross (×) is the multiplication symbol and it is used to denote multiplication in a mathematical expression.
4. What is the Long Division Method of Division and how to perform it?
The Long Division Method is one of the methods used to solve Division problems. InLong Division Method, the divisor is noted outside the right parenthesis. The dividend is placed inside it and the quotient is written outside the overbar, on top of the dividend's place In mathematics, the result of the division between a number and any divisor is called a quotient. The quotient is the number of times that the divisor is included in the dividend without the division's remainder being negative. The steps to perform Long Division Method are-
First Step- Firstly, take the first digit of the dividend and check if this digit is greater or equal to the divisor.
Second Step- Then divide it by the divisor and write the answer on top.
Third Step- Now, subtract the above result from the digit and note below.
Fourth Step- Lastly repeat the same process till the remainder is 0.
5. How To Solve Subtraction Problems?
Subtraction is a mathematical function that is used to find the difference between numbers. To solve problems of subtraction, one splits the numbers into columns using their respective place values: ones, tens, hundreds, etc. While solving Subtraction Questions, there are cases where the subtraction is only possible with borrowing from the bigger number. Subtraction Regrouping is another term given to subtraction. If the minuend ( the number from which the other number is going to be subtracted)is smaller than the subtrahend (the number which is going to be subtracted from the minuend), the Regrouping method is used. In this method of regrouping, one number is borrowed from the prior column to cause the minuend to have a greater value than the subtrahend. This is how subtraction is solved.