Factors of 33: 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 33, a composite number, and explore the various ways in which it can be broken down into its component parts.

## Contents

**Factors Calculator**

**Factors of 33 Details**

Factors of 33: 1, 3, 11 and 33

Negative Factors of 33: -1, -3, -11 and -33

Prime Factors of 33: 3, 11

Prime Factorization of 33: 3 × 11

Factors of 33 in Pairs: (1, 32) and (3, 11)

Negative Pairs Factors of 33: (-1, -33) and (-3, -11)

**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.

**Factors of 33**

Now that we have a basic understanding of prime and composite numbers, let’s take a closer look at the factors of 33. A factor of a number is a whole number that divides evenly into the number without leaving a remainder. In the case of 33, its factors include 1, 3, 11, and 33.

**1 as a Factor**

Every number, including 33, has 1 as a factor. This is because any number multiplied by 1 will equal itself. Therefore, 1 is always a factor of any given number.

**3 as a Factor**

Another factor of 33 is 3. This is because 33 can be evenly divided by 3, with a quotient of 11. In other words, 33 ÷ 3 = 11.

**11 as a Factor**

As we have already established, 11 is also a factor of 33. This is because 33 can be evenly divided by 11, with a quotient of 3. In other words, 33 ÷ 11 = 3.

**33 as a Factor**

Finally, 33 is also a factor of 33. This may seem obvious, but it is important to note that a number is always a factor of itself.

## Factor pairs of 33

1 x 33 = 33

3 x 11 = 33

So, (1, 33) and (3, 11) are factor pairs of 32 Factor pairs of -32

-1 x -33 = 33

-3 x -11 = 33

So, (-1, -33) and (-3, -11) are negative pair factors of 32

## Prime Factorization of 33

33 ÷ 11 = 3

3 ÷ 3 = 1

Therefore, 3 x 11 are Prime factorization of 32.

## Factor tree of 33

```
33
/ \
3 11
```

Factors of 3 |

Factors of 6 |

Factors of 11 |

Factor Pairs of 10 |

Factors of 34 |

Factor Pairs of 60 |

Factor Pairs of 66 |