Understanding Prime and Composite Numbers When studying mathematics, one of the fundamental concepts that students learn is that of prime and composite numbers. In this article, we will delve into the factors of 40, a composite number, and explore the various ways in which it can be broken down into its component parts.

## Contents

**Factors Calculator**

Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40

Negative Factors of 40: -1, -2, -4, -5, -8, -10, -20 and -40

Prime Factors of 40: 2, 5

Prime Factorization of 40: 2 × 2 × 2 × 5

Factors of 40 in Pairs: (1, 40), (2, 20), (4, 10) and (5, 8)

Negative Pairs Factors of 40: (-1,-40), (-2,-20), (-4,-10), (-5,-8)

**Prime Numbers**

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Some examples of prime numbers include 2, 3, 5, 7, and 11. Prime numbers are important in mathematics as they are used in many mathematical formulas and algorithms, and are also used in the study of number theory.

**Composite Numbers**

A composite number is a whole number greater than 1 that can be divided evenly by a number other than 1 or itself. In other words, a composite number is not a prime number. Some examples of composite numbers include 4, 6, 8, 9, and 10.

## What are the factors of 40?

The method of calculating the factors of 40 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 40 are the factors of 40.

By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 40 ÷ 1 = 40

This division gives the remainder 0 and so is divisible by 40. So please put them 1 and 40 in your factor list.

1, …….. 40

(ii) 40 ÷ 2 = 20

This division gives the remainder 0 and so is divisible by 20. So please put them 2 and 20 in your factor list.

1, 2 …….. 20, 40

(iii) 40 ÷ 3 = 13.33

This division gives the remainder 13.33, not being thoroughly divided. So we will not write 3 and 13.33 on the list.

(iv) 40 ÷ 4 = 10

This division gives the remainder 0 and so is divisible by 10. So please put them 4 and 10 in your factor list.

1, 2, 4 …….. 10, 20, 40

(iv) 40 ÷ 5 = 8

This division gives the remainder 0 and so is divisible by 10. So please put them 5 and 8 in your factor list.

1, 2, 4, 5 …….. 8, 10, 20, 40

(v) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

So 1, 2, 4, 5, 8, 10, 20 and 40 are factors of 40.

## Factor pairs of 40

1 x 40 = 40

2 x 20 = 40

4 x 10 = 40

5 x 8 = 40

So, (1, 40), (2, 20), (4, 10) and (5, 8) are factor pairs of 40

## Factor pairs of -40

-1 x -40 = 40

-2 x -19 = 40

-4 x -10 = 40

-5 x -8 = 40

So, (-1,-40), (-2,-20), (-4,-10) and (-5,-8) are negative pair factors of 40

## Prime Factorization of 40

40 ÷ 2 = 20

20 ÷ 2 = 10

10 ÷ 2 = 5

5 ÷ 5 = 1

Therefore, 2 × 2 × 2 × 5 are Prime factorization of 40.

## Factor tree of 40

```
40
/ \
2 20
/ \
2 10
/ \
2 5
```

**More List of Factors**

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