Divisor
A divisor is a number that divides another number. Without a divisor, we cannot divide numbers. In division, there are four important terms that are used  dividend, divisor, quotient, and remainder. Division is a method of distributing objects equally in groups. The number that needs to be divided is known as the 'dividend' and the total number of equal groups in which it has to be divided is called the 'divisor'. The number that is left out without forming a group is termed as the 'remainder'.
1.  What is a Divisor? 
2.  How to Find the Divisor? 
3.  Divisor Formula 
4.  Divisor Facts 
5.  Difference Between Divisor and Factors 
6.  FAQs on Divisors 
What is a Divisor?
A divisor divides a number into equal groups. The number that is being divided is called the dividend and the number that divides it is called the divisor.
Divisor Meaning
A number that divides another number with or without leaving a remainder is called a divisor.
There are different ways to write a division problem. The following figure shows the different ways in which division is expressed and it shows how to identify the divisor, the dividend and the quotient.
How to Find the Divisor?
Without divisors, division is not possible. This means identifying a divisor is quite simple. For example, if we need to divide the number 35 by 5, it can be represented as 35 ÷ 5 = 7. Here, the number 35 is the dividend, the number 5 is the divisor, and the number 7 is the quotient.
Sometimes we know the value of the dividend and the quotient and we need to find the divisor. In that case, we use the divisor formula. Let us learn about the divisor formula in the following section.
Divisor Formula
The divisor formula is formed for two situations  with or without a remainder:
 If the remainder is 0, then Divisor = Dividend ÷ Quotient.
 If the remainder is not 0, then Divisor = (Dividend  Remainder) ÷ Quotient
Example 1: Find the divisor if the dividend is 48 and the quotient is 4.
Solution: We know that dividend = 48, quotient = 4. So, let us apply the divisor formula, Divisor = Dividend ÷ Quotient. Substituting the known values in the formula, we get, Divisor = 48 ÷ 4 = 12. Therefore, the divisor = 12.
Example 2: Find the divisor if the dividend is 59, the quotient is 11 and the remainder is 4.
Solution: We know that dividend = 59, quotient = 11, remainder = 4. So, let us apply the divisor formula, Divisor = (Dividend  Remainder) ÷ Quotient. Substituting the known values in the formula, we get, Divisor = (59  4) ÷ 11 = 55 ÷ 11 = 5. Therefore, the divisor = 5.
Divisor Facts
Here is a list of a few facts related to the divisor.
 When the quotient is the same as the dividend then the divisor is 1. For example, 45 ÷ 1 = 45
 When the dividend and the divisor are equal in a division problem, the quotient is 1. For example, 45 ÷ 45 = 1
 A quotient is a number that is obtained upon dividing a dividend by a divisor, and any number that is left over after the division is called the remainder.
 The remainder is always smaller than the divisor.
 When the remainder is zero it means the divisor has completely divided the dividend.
 When the divisor is greater than the dividend, then the resultant number will be a decimal number. For example, 45 ÷ 100 = 0.45
Difference Between Factor and Divisor
We know that divisor is a number that divides the dividend. When a divisor divides the dividend completely and leaves no remainder, that divisor is also called a factor of that number. Thus, all factors of a number are divisors but all divisors need not be factors of a number always.
Example 1: Factors of 8 = 1, 2, 4, and 8. This means 8 is completely divisible by 1, 2, 4, 8. Therefore, all these factors are divisors in this case.
Example 2: Divide 12 by 5. If we divide 12 by 5 we get 2 as the quotient and the remainder is 2. This means 12 ÷ 5 = 2, Remainder = 2. In this case, the divisor is 5, but 12 is not completely divisible by 5. So, 5 is not a factor of 12 but it is a divisor of 12 as it gives a remainder of 2.
Hence, all factors are divisors but all divisors are not factors.
Important Tips on Divisor
Given below are some of the important tips related to the divisor that we studied in this article.
 A divisor cannot be zero because when a number is divided by zero the result is undefined.
 A division problem stays true even if we swap the quotient and the divisor.
 When zero is divided by any divisor it always gives zero as the quotient.
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Divisor Examples

Example 1: Find the divisor when the dividend is 7560 and the quotient is 63.
Solution:
It is given that the dividend = 7560, quotient = 63. So, let us apply the divisor formula, Divisor = Dividend ÷ Quotient. Substituting the known values in the formula, we get, Divisor = 7560 ÷ 63 = 120. Therefore, the divisor = 120.

Example 2: What is the divisor if the dividend is 675, the quotient is 12 and the remainder is 3?
Solution:
It is given that the dividend = 675, quotient = 12, remainder = 3. So, let us apply the divisor formula, Divisor = (Dividend  Remainder) ÷ Quotient. Substituting the known values in the formula, we get, Divisor = (675  3) ÷ 12 = 672 ÷ 12 = 56. Therefore, the divisor = 56.

Example 3: State true or false.
a.) A number that divides another number is called a divisor.
b.) In the statement, 84 ÷ 12 = 7, the divisor is 84.
Solution:
a.) True, a number that divides another number is called a divisor.
b.) False, in the statement, 84 ÷ 12 = 7, the divisor is 12, and 84 is the dividend.
FAQs on Divisors
What is a Divisor in Math?
A number that divides another number is known as the divisor. For example, when we divide 20 by 4 we get 5. When we write it as, 20 ÷ 4 = 5, here 4 is the number that is dividing the number 20. Therefore, 4 is known as the divisor.
Is a Number a Divisor of Itself?
Yes, a number is a divisor of itself because a number can divide itself completely. This means that it will give the quotient as 1. For example, 23 ÷ 23 = 1
What is the Divisor in a Fraction?
A fraction is represented in the form p/q, (where q is not equal to 0). Here, the denominator q is the divisor. For example, in the fraction 6/2, the denominator 2 is the divisor.
What is the Formula of Divisor?
We use the divisor formula when we know the value of the dividend and the quotient. We have two scenarios to find the divisor.
 If the remainder is 0, then Divisor = Dividend ÷ Quotient.
 If the remainder is not 0, then Divisor = (Dividend  Remainder) ÷ Quotient
What is the Divisor in the Division Fact 30 ÷ 15 = 2?
Divisor is the number that divides another number. Here 30 is divided by 15. Therefore,15 is the divisor.
What is the Difference Between Divisor and Dividend?
A divisor divides a number into equal groups. The number that is being divided is called the dividend and the number that divides it is called the divisor. For example, in 72 ÷ 6 = 12, 72 is the dividend and 6 is the divisor.
What is the Greatest Common Divisor?
The Greatest Common Divisor (GCD) refers to the greatest positive number that is a common divisor for a given set of positive numbers. It is also known as the Highest Common Factor (HCF) or the Greatest Common Factor (GCF). For example, let us find the greatest common divisor of 10 and 22. We will list the divisors of 10 and 22. Divisors of 10 = 1, 2, 5, 10. Divisors of 22 = 1, 2, 11, 22. The common divisors of 10 and 22 = 1, 2. The greatest common divisor = 2.
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