# 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:

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

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:

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

## Practice Problems

### 1If 3 is the divisor, which of these would give the remainder as 2?

37
47
57
67
CorrectIncorrect
Correct answer is: 47
47 is the correct answer as it gives a remainder of 2 when divided by 3.
37 ÷ 3 = 12 R1
47 ÷ 3 = 15 R2
57 ÷ 3 = 19
67 ÷ 3 = 22 R1

### 2Which of the following has the most number of divisors?

44
36
29
47
CorrectIncorrect
Correct answer is: 36
36 has the most number of divisors.
Divisors of 44: 1, 2, 4, 11, 22, 44.
Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Divisors of 29: 1 and 29
Divisors of 47: 1 and 47

### 3What is the greatest common divisor of 13 and 30?

3
2
1
13
CorrectIncorrect
Correct answer is: 1
Divisors of 13: 1 and 13
Divisors of 30: 1, 2, 3, 10, 15, 30
Common divisor of 13 and 30:
1 Greatest Common Divisor of 13 and 30: 1

### 4Which of the following is NOT a factor of 14?

1
2
4
7
CorrectIncorrect
Correct answer is: 4
Factors of 14 are: 1, 2, 7, 14.

## Frequently Asked Questions

When we divide two numbers, the number that is being divided is the dividend, whereas the number by which we divide is the divisor. For example, 12 candies are to be divided among 3 children. So we have 12 ÷ 3. Here, 12 is the dividend, and 3 is the divisor.

A divisor is any number that divides another number. A factor, however, is a divisor that divides the number entirely and leaves no remainder.

Yes, all numbers are divisors of themselves. This is because every number divides itself and gives 1 as the quotient. For example, if we have 12 ÷ 12, then 12 becomes the divisor of 12, and 1 becomes the quotient.

If the remainder is 0, then Divisor = Dividend ÷ Quotient. If the remainder is not 0, then Divisor = (Dividend – Remainder) /Quotient.