# Proper Divisors. What is a proper divisor and how to work them out?

A proper divisor of a number is a positive whole number that divides exactly into the number except from itself.

So in order to work out all the proper divisors of a number first find all the divisors of your number then exclude the largest divisor (itself).

Letâ€™s take a look at some examples:

**Example 1**

Write down all the proper divisors of 10.

First work out all of the divisors of 10. These are:

1,2,5 and 10 (since 10 can be divided by all these numbers without giving remainders).

So the proper divisors of 10 are:

1, 2 and 5 (just exclude itself).

**Example 2**

Write down all the proper divisors of 21.

First work out all of the divisors of 21. These are:

1,3,7 and 21 (since 21 can be divided by all these numbers without giving remainders).

So the proper divisors of 21 are:

1, 3 and 7 (just exclude itself).

**Example 3**

Write down all the proper divisors of 40.

First work out all of the divisors of 40. These are:

1, 2, 4, 5, 8, 10, 20 and 40 (since 40 can be divided by all these numbers without giving remainders).

So the proper divisors of 40 are:

1, 2, 4, 5, 8, 10 and 20 (just exclude itself).

**Example 4**

Write down all the proper divisors of 16.

First work out all of the divisors of 16. These are:

1, 2, 4, 8 and 16 (since 16 can be divided by all these numbers without giving remainders).

So the proper divisors of 16 are:

1,2,4,8 and 16 (just exclude itself).

**Example 5**

Write down all the proper divisors of 3.

First work out all of the divisors of 3. These are:

1 and 3 (since 3 can be divided by all these numbers without giving remainders).

So there is only one proper divisor of 3 which is 1.

**Summary**

The proper divisors are the same as the divisors of a number excluding itself.

## More by this Author

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

## Comments

No comments yet.