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 45, a composite number, and explore the various ways in which it can be broken down into its component parts.

## Contents

## Factors Calculator

Factors of 45: 1, 3, 5, 9, 15 and 45

Negative Factors of 45: -1, -3, -5, -9, -15 and -45

Prime Factors of 45: 3, 5

Prime Factorization of 45: 3 × 3 × 5

Factors of 45 in Pairs: (1, 45), (3, 15) and (5, 9)

Negative Pairs Factors of 45: (-1, -45), (-3, -15) and (-5, -9)

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 45?

The method of calculating the factors of 45 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 45 are the factors of 45.

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

(i) 45 ÷ 1 = 45

This division gives the remainder 0 and so is divisible by 45. So please put them 1 and 45 in your factor list.

1, …. 45

(ii) 45 ÷ 2 = 22.5

This division gives the remainder 22.5, not being thoroughly divided. So we will not write 2 and 22.5 on the list.

(iii) 45 ÷ 3 = 15

This division gives the remainder 0 and so is divisible by 15. So please put them 3 and 15 in your factor list.

1, 3 …. 15, 45

(iv) 45 ÷ 4 = 11.25

This division gives the remainder 11.25, not being thoroughly divided. So we will not write 4 and 11.25 on the list.

(iv) 45 ÷ 5 = 9

This division gives the remainder 0 and so is divisible by 15. So please put them 3 and 15 in your factor list.

1, 3, 5 …. 9, 15, 45

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

So 1, 3, 5, 9, 15 and 45 are factors of 45.

## Factor pairs of 45

1 x 45 = 45

3 x 15 = 45

5 x 9 = 45

So, (1, 45), (3, 15) and (5, 9) are factor pairs of 45

## Factor pairs of -45

-1 x -45 = 45

-3 x -15 = 45

-5 x -9 = 45

So, (-1, -45), (-3, -15) and (-5, -9) are negative pair factors of 45

## Prime Factorization of 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 5 = 1

Therefore, 3 × 3 × 5 are Prime factorization of 45.

## Factor tree of 45

```
45
/ \
3 15
/ \
3 5
```

Factors of 3 |

Factors of 6 |

Factors of 11 |

Factor Pairs of 10 |

Factors of 33 |

Factors of 38 |

Factors of 44 |

Factors of 46 |

Factor Pairs of 60 |

Factor Pairs of 66 |