Factors of 27 are the list of positive and negative whole numbers that can be divided evenly into 27. Negative factors of 27 are just factors with a negative sign. Did you know? There are 27 cubes in a Rubik's Cube. In this lesson, we will learn to determine the factors of 27 along with its prime factors and its factors in pairs. We will also solve some examples and interactive questions for a better understanding.

**Factors of 27:**1, 3, 9, and 27**Factors of -27:**-1, -3, -9, and -27**Prime Factorization of 27:**27 = 3^{3}

**Table of Contents**

- What are Factors of 27?
- How to Calculate Factors of 27?
- Important Notes
- Factors of 27 by Prime Factorization
- Challenging Questions
- Factors of 27 in Pairs
- Tips and Tricks
- FAQs on Factors of 27
- Factors of 27 Solved Examples
- Interactive Questions

## What are Factors of 27?

Let us recall the meaning of the term "factor." Factors of a number are the numbers that, when multiplied together, give the original number:

- Factors of a number are numbers that divide the original number completely without leaving any remainder.
- If the factors of a number are prime numbers, then the factors are said to be prime factors.
- There can be many factors of a number.

A **factor** is a number that divides a given number into equal parts. 3 and 9 are the factors of 27, that is, 3 divides 27 into equal parts of 9 each.

3 × 9 = 27

27 does not have 9 and 3 as its only factors. It has other factors as well. Let us see how to calculate the factors of 27.

## How to Calculate the Factors of 27?

Let us learn how to calculate the factors of 27.

**Step 1:**Write down the number to be factored, i.e., 27.**Step 2:**Find the two numbers whose product gives 27.

For example:

- Let's say we take 3 and 9 to be the two factors.
- 3 is a prime number. Hence, it can only be factored as 1 and the number itself, i.e., 3.
- 3 can be written as 3 × 1 = 3
- 9 is not a prime number. Hence, it can be factorized as a product of 3 and 3, apart from the product of 1 and the number itself, i.e., 9.
- 9 can be written as 3 × 3 = 9
- Thus, 27 can be written as 27= 3 × 3 × 3

Hence, the factors of 27 are **1, 3, 9,** and **27**. Explore factors using illustrations and interactive examples:

- Factors of 270 - The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
- Factors of 23 - The factors of 23 are 1, 23
- Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28
- Factors of 12 - The factors of 12 are 1, 2, 3, 4, 6, 12
- Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

**Important Notes:**

- Factors of any number are all the possible numbers it is divisible by. They may be prime numbers or composite numbers.
- Factors are never fractions or decimals.
- Factors can be negative.

## Factors of 27 by Prime Factorization

**Prime factorization** is the process of writing a number as a product of its prime factors. Let us learn how to find factors using prime factorization.

**Step 1:**Write the pair of factors, which on multiplication, gives the required number.**Step 2:**See the factors, whether each one of them is prime or not.**Step 3:**Follow the below criterion to differentiate between the factorization procedure.

- If both the numbers are prime, they can be multiplied as they are.
- If one among them is prime and another one is composite, then the composite number is dissociated into its factors.
- If both the numbers are composite, they can be dissociated into factors.

**Factors of 27 by prime factorization are given using the following steps.**

**Step 1:**Write the pair of factors which, on multiplication, gives the required number.- 27 can be factored as a product of 3 and 9.
**Step 2:**See the factors, whether each one of them is prime or not.- 9 is not a prime number and can be dissociated as a product of 3 by 3 or as a square of 3.
- 3 is a prime number, hence doesn't need any further dissociation.
**Step 3:**As per the criterion, 27 can be written as**27 = 9 × 3 = 3 × 3 × 3**. It can also be written as**27 = 3**^{3}

Factors of 18 can be found in a similar way. Let's see how:

**Step 1:**Write the pair of factors which, on multiplication, gives the required number.- 18 can be factored as a product of 3 and 6.
**Step 2:**See the factors, whether each one of them is prime or not.- 3 is a prime number, hence doesn't need any further dissociation.
- 6 is not a prime number and can be dissociated as a product of 2 and 3.

Therefore, 18 can be written as** 18 = 3 × 6 = 3 × 3 × 2.** It can also be written as **18 = 3 ^{2} × 2**

**Challenging Questions:**

- What are the factors of the following numbers using the prime factorization method?

- 98
- 235
- 4500

## Factors of 27 in Pairs

Pair factors are pairs of factors of a number that, when multiplied, give the product as the original number. Here the required number is 27. Let's try visualizing it using blocks:

**Positive pair factors of 27:**

Factors |
Pair Factors |

1 × 27 = 27 | 1, 27 |

3 × 9 = 27 | 3, 9 |

9 × 3 = 27 | 9, 3 |

27 × 1 = 27 | 27, 1 |

**Let's have a look at Negative pair factors:**

Factors |
Pair Factors |

-1 × -27 = 27 | -1, -27 |

-3 × -9 = 27 | -3, -9 |

-9 × -3 = 27 | -9, -3 |

-27 × -1 = 27 | -27, -1 |

**Tips and Tricks:**

- 1 is the smallest factor of every number.
- Every number has a minimum of two factors, i.e., 1 and the number itself.
- All even numbers always have 2 as one of their factors.
- All the numbers which end in 5 will always have 5 as one of their factors.
- All the numbers which end in 0 will always have 1, 2, 5, and 10 as their factors.

## FAQs on Factors of 27

### How many Factors are there in 27?

Positive factors of 27 are 1, 3, 9, 27. Therefore, there are four positive factors of 27.

### Is 9 a Factor of 27? Yes or no.

Yes. Since 9 divides 27 completely and leaves no remainder, it is a factor of 27.

### What is the Perfect Square of 27?

27 × 27 = 729. Therefore, the **perfect square** of 27 is 729.

### What are the Factors of 28?

The factors of 28 are 1, 2, 4, 7, 14, and 28.

### What are the Common Factors of 27 and 36?

Factors of 27 = 1, 3, 9, 27 and the factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

Thus, the common factors of 27 and 36 are 1, 3, and 9.

## Factors of 27 Solved Examples

**Example 1: **Three friends plucked 27 mangoes from a tree and distributed among themselves equally. How many would each one of them get?

**Solution:**

27 mangoes are to be divided among 3 friends equally. This implies we need to divide 27 by 3.

- 27/3 = 9

Hence, each child will get 9 mangoes.

**Example 2: **Help John find the positive pairs of factors of 36.

**Solution:**

Positive pair factors of 36 are given as:

Factors |
Pair Factors |

1 × 36 = 36 | 1, 36 |

2 × 18 = 36 | 2, 18 |

3 × 12 = 36 | 3, 12 |

4 × 9 = 36 | 4, 9 |

6 × 6 = 36 | 6, 6 |

9 × 4 = 36 | 9, 4 |

12 × 3 = 36 | 12, 3 |

18 × 2 = 36 | 18, 2 |

36 × 1 = 36 | 36, 1 |

Hence, John has found the positive pairs of factors of 36.

**Example 3: **Which number on multiplying with -6 gives 48?

**Solution:**

The negative factor pairs of 48 are:

**(-1, -48), (-2, -24),(-3, -16),(-4, -12), (-6, -8)**

Therefore when -8 is multiplied by -6, the product is 48 i.e. -6 × -8 = 48.

**Example 4: **Anna has 54 units of a cutlery set. She wants to pack it in cartons such that these units are evenly distributed. There are two sizes of cartons available to her. One size has a capacity of 9 units and the other size has a capacity of 12 units. Which size of the carton will she choose so that there is no unit left and maximum units are filled in the cartons?

**Solution:**

The units must be evenly distributed and no units should be left behind. This implies the number of units in each carton must be a factor of 54.

- The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

12 is not a factor of 54 whereas 9 is a factor of 54. Hence, Anna will choose the carton with a capacity of 9 units.

**Example 5: **A rectangle has an area of 40 square inches and a length of 10 inches. Determine its breadth.

**Solution:**

The area of the rectangle is length × breadth. The length of the rectangle, i.e., 10 inches, is a factor of the area, i.e., 40 square inches.

When 4 is multiplied by 10, the product is 40 i.e. 4 × 10 = 40

Therefore, the breadth of the rectangle is 4 inches.

## Interactive Questions

**Here are a few activities for you to practice. **

**Select/Type your answer and click the "Check Answer" button to see the result.**