Common Core Math Vocabulary

Divisor - Definition with Examples

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 

division equation of divisor

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: 

different ways of represent divisor 


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 Facts

  • If we double the divisor, the quotient will be half.

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