Factors of 36: 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 36, a composite number, and explore the various ways in which it can be broken down into its component parts.

## Contents

## Factors Calculator

To find the factors of a number, you can use a factors calculator. These calculators are simple tools that allow you to input a number and find its factors in seconds. While it’s easy to use a calculator, it’s also important to understand how to find the factors of a number manually, as this will help you build your math skills.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36

Negative Factors of 36: -1, -2, -3, -4, -6, -9, -12, -18, and -36

Prime Factors of 36: 2, 3

Prime Factorization of 36: 2 × 2 × 3 × 3

Factors of 36 in Pairs: (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6)

Negative Pairs Factors of 36: (-1, -36), (-2, -18), (-3, -12), (-4, -9) and (-6, -6)

**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 36?

The method of calculating the factors of 36 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 36 are the factors of 36.

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

(i) 36 ÷ 1 = 36

This division gives the remainder 0 and so is divisible by 36. So please put them 1 and 36 in your factor list.

1, …….. 36

(ii) 36 ÷ 2 = 16

This division gives the remainder 0 and so is divisible by 18. So please put them 2 and 18 in your factor list.

1, 2 …….. 18, 36

(iii) 36 ÷ 3 = 12

This division gives the remainder 0 and so is divisible by 12. So please put them 3 and 12 in your factor list.

1, 2, 3 …….. 12, 18, 36

(iv) 36 ÷ 4 = 9

This division gives the remainder 0 and so is divisible by 9. So please put them 4 and 9 in your factor list.

1, 2, 3, 4 …….. 9, 12, 18, 36

(iv) 36 ÷ 5 = 7.2

This division gives the remainder 7.2, not being thoroughly divided. So we will not write 5 and 7.2 on the list.

(iv) 36 ÷ 6 = 6

This division gives the remainder 0 and so is divisible by 6. So please put them 6 in your factor list.

1, 2, 3, 4, 6 …….. 9, 12, 18, 36

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

So 1, 2, 3, 4, 6, 9, 12, 18, and 36 are factors of 36.

### Factor pairs of 36

1 x 36 = 36

2 x 18 = 36

3 x 12 = 36

4 x 9 = 36

6 x 6 = 36

So, (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6) are factor pairs of 36

### Factor pairs of -36

-1 x -36 = 36

-2 x -18 = 36

-3 x -12 = 36

-4 x -9 = 36

-6 x -6 = 36

So, (-1, -36), (-2, -18), (-3, -12), (-4, -9) and (-6, -6) are negative pair factors of 36

### Prime Factorization of 36

36 ÷ 2 = 18

18 ÷ 2 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

Therefore, 2 × 2 × 3 × 3 are Prime factorization of 36.

### Factor tree of 36

```
36
/ \
2 18
/ \
2 9
/ \
3 3
```

Factors of 3 |

Factors of 6 |

Factors of 11 |

Factor Pairs of 10 |

Factors of 33 |

Factors of 38 |

Factor Pairs of 60 |

Factor Pairs of 66 |