# Divisor – Definition, Examples, Practice Problems, FAQs

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## 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 On Divisor

1

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

37
47
57
67
CorrectIncorrect
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
2

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

44
36
29
47
CorrectIncorrect
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
3

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

3
2
1
13
CorrectIncorrect
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
4

1
2
4
7
CorrectIncorrect