Divisor – Definition, Formula, Properties, Facts, Examples, Facts

What Is a Divisor in Math?

In division, the divisor is the number by which the dividend is divided to obtain the quotient. 

A number that divides another number either completely or partially is known as a divisor. In other words, a divisor in a division problem is a number we divide another number by. 

Divisor Examples:

What is Division?

Division is a mathematical operation that involves splitting a quantity or number into equal parts or groups.

Example: Divide 20 balls equally into five boxes.

This is defined by a division problem: $20 \div 5$

$20 \div 5 = 4$

Each box gets 4 balls.

Dividend, Divisor, Quotient, and Remainder

Four important parts in any division problem are: 

Dividend, Divisor, Quotient and Remainder.

• Dividend is the number or quantity being divided. 
• Divisor is the number by which we divide the dividend.
• Quotient is the answer to the division problem. It is the number which we get by dividing a number. 
• Remainder is the number which is left after dividing the two numbers. 

Example 1:

Example 2: $30 \div 7$

Dividend $= 30$

Divisor $= 7$

Quotient $= 4$

Remainder $= 2$

How to Identify the Divisor

Identifying a divisor is quite simple. It is the number by which a given number (dividend) is divided.

Example: If we divide the number 45 by 9, it can be represented as $45 \div 9$. 

Here, 45 is the dividend.

We are dividing 45 by 9.

Thus, 9 is the divisor. 

There are different ways to write a division problem. Let’s understand the different parts of the division in each case.

What Does the Divisor Represent in a Division?

As mentioned earlier, in the division problem, we break a large number into equal groups.

Divisor is the quantity that determines the number of equal parts or groups the dividend is divided into. The divisor indicates the size or magnitude of each part or group.

Divisor Formula

The relationship between the dividend, divisor, quotient and remainder is given by

We can also write this as

Dividend = (Divisor × Quotient) + Remainder

Using this equation, we can define the divisor formula.

Let’s discuss two situations – with or without a remainder:

When remainder = 0	When remainder 0
Divisor = Dividend ÷ Quotient	Divisor = (Dividend – Remainder) ÷ Quotient

Properties of Divisor

1) Zero cannot be a divisor.

2) When the divisor is 1, the quotient equals the dividend.

3) When the dividend is the same as the quotient, the divisor = 1. 

Example: 65 ÷ 1 = 65. 

4) When the dividend equals the divisor, then the quotient = 1.

Example: 65 ÷ 65 = 1.

5) The remainder is always less than the divisor. 

Difference between Divisors and Factors

In a division problem, the term ‘divisor’ refers to the number that divides the dividend. It does not matter if the remainder is zero or non-zero. 

A factor is a positive integer that divides a given number exactly, leaving no remainder. Thus, if the divisor evenly divides the dividend with 0 remainder, the divisor is termed as the factor of that particular number. 

A factor of any number is a special case where the remainder of division is 0.

Special Divisors: Division by Powers of 10

• When the divisor is 10, the decimal point will move one place to the left.

Example: $15 \div 10 = 1.5$

• When the divisor is 100, the decimal point will move two places to the left.

Example: $256 \div 100 = 2.56$

• When the divisor is 1000, the decimal point will move three places to the left.

Example: $345 \div 1000 = 0.345$

Facts about Divisor

Conclusion

In this article, we learned about divisors, how to identify divisors, their properties, and different parts of division. We also discussed how different powers of 10 act as special divisors. Let’s solve a few examples and practice MCQs for better comprehension.

Solved Examples on Divisor

1. Identify dividend and divisor in each division problem.

i) 108 ÷ 12 

ii) 24 ÷ 5

iii) 200 ÷ 10

iv) 7 ÷ 2

Solution:

Sr. No.	Division problem	Dividend	Divisor
i)	108 ÷ 12	108	12
ii)	24 ÷ 5	24	5
iii)	200 ÷ 10	200	10
iv)	7 ÷ 2	7	2

2. Define the parts of division when 729 is divided by 9.

Solution:

729 is divided by 9.

Dividend is the number being divided.

Dividend = 729

Divisor is the number we divided the dividend by.

Divisor = 9

Let’s divide.

$72 \div 99 = 81$

Thus, quotient = 81

Remainder = 0

3. Alex distributed 12 strawberries equally. Everybody got only 1 strawberry. What is the divisor and what does the divisor represent? 

Solution:

Number being divided = 12

Everybody got only 1 strawberry.

So, quotient = 1

Here, the divisor is the number of groups or the total number of equal parts of 12. 

Since the quotient is 1, Alex actually divided 12 strawberries into 12 equal parts (friends), such that each person got 1 strawberry.

Practice Problems on Divisor

Frequently Asked Questions On Divisor