# What are the multiples of 6?

A **perfect number** is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. **Six** is the smallest perfect number because it has divisors of 1, 2, and 3, which if we add together, the sum is also 6.

The number six (6) is a **natural number** that comes after five and before seven. It is also the second smallest composite number after 4. Six is an interesting number, isn’t it?

Now… let’s take an adventure to see the wonders and beauty of this fascinating number.

## Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54 …

When we talk about multiples of 6, we are talking about the numbers that when divided by 6 it will have a **zero remainder**. To properly define it, a **multiple of 6** is a product of 6 and any natural number. More so, the difference between two consecutive of 6 will always be 6.

## 6 as a Factor and Multiple

**Multiples** are the *n*-times of any integer. On the other hand, **factors** are the numbers that, when multiplied together, generate an original number.

There are infinitely many multiples of 6, but the factors of 6 are fixed. We only have 4 exact factors – 1, 2, 3, and 6, while its multiples are 6, 12, 18, 24, 30, and so on.

Furthermore, since 2 and 3 are factors of 6, we can say that all multiples of 6 are also multiples of 2 and 3. However, not all multiples of 2 and 3 are multiples of 6.

Multiples of 2, 3, and 6 | Multiples of 2 that are not multiples of 6 | Multiples of 3 that are not multiples of 6 |
---|---|---|

All multiples of 6 are also multiples of 2 and 3 such as 6, 12, 18, 24, 30, etc. | 2, 4, 8, 10, 14, etc. are multiples of 2 but not multiples of 6. | 3, 9, 15, 21, 27 are some of the multiples of 3 that are not multiple of 6. |

## Did you know that…

Aside from being the smallest perfect number, six (6) is also the only number that is both the sum and product of three consecutive positive numbers – 1, 2, 3.

How cool is that?

## How to Determine the Multiples of 6?

We’ve already defined what it means when we say a number is a multiple of 6. Now, we are going to determine how we can find the possible multiples of 6. There are two ways on how we can find the multiples of 6 – by **skip counting** or **multiplication**.

### Skip Counting

Skip counting by 6 is one way to find the multiples of 6. This is done by repeatedly adding 6 as many times as you want. For example, to get the first 5 multiples of 6, we start by 6. Then, to get the next term, we will add another 6 to 6. Hence, **6 + 6 = 12**.

Continuing this process, we will have the result same as the diagram below.

This process is recommended to use if you are only looking for the first 5 or 10 multiples of 6… but if you are looking for the 1000^{th} or 499^{th} multiple of 6, this process will be time-consuming.

### Multiplication

Any number that can be represented as 6*n*, where *n* is an integer, is a multiple of 6. Thus, to find the multiples of 6, we will just multiply any natural number to 6.

Say, for example, the 50^{th} positive multiple of 6 is determined by simply multiplying 50 and 6. Hence, **50 x 6 = 300**.

Similarly, if we are going to find the 99^{th} negative multiple of 6, we will multiply -99 and 6. Thus, **-99 x 6 = -594**.

It’s very simple, right?

Now, let’s take a look at how these two methods differ from each other.

### Skip Counting vs. Multiplication

The table below shows how we can determine the n^{th} multiple by skip counting and multiplication. Which method do you prefer to use, and why?

n^{th }Multiple | Skip Counting | Multiplication |
---|---|---|

1^{st} multiple | 6 | 6 x 1 = 6 |

2^{nd} multiple | 6 + 6 = 12 | 6 x 2 = 12 |

3^{rd} multiple | 6 + 6 + 6 = 18 | 6 x 3 = 18 |

4^{th} multiple | 6 + 6 + 6 + 6 = 24 | 6 x 4 = 24 |

5^{th} multiple | 6 + 6 + 6 + 6+ 6 = 30 | 6 x 5 = 30 |

## List of the First 30 Multiples of 6

Let’s take a look at this table that shows the first 30 multiples of 6.

Product of 6 and a positive counting number | Multiples of 6 |
---|---|

6 x 1 | 6 |

6 x 2 | 12 |

6 x 3 | 18 |

6 x 4 | 24 |

6 x 5 | 30 |

6 x 6 | 36 |

6 x 7 | 42 |

6 x 8 | 48 |

6 x 9 | 54 |

6 x 10 | 60 |

6 x 11 | 66 |

6 x 12 | 72 |

6 x 13 | 78 |

6 x 14 | 84 |

6 x 15 | 90 |

6 x 16 | 96 |

6 x 17 | 102 |

6 x 18 | 108 |

6 x 19 | 114 |

6 x 20 | 120 |

6 x 21 | 126 |

6 x 22 | 132 |

6 x 23 | 138 |

6 x 24 | 144 |

6 x 25 | 150 |

6 x 26 | 156 |

6 x 27 | 162 |

6 x 28 | 168 |

6 x 29 | 174 |

6 x 30 | 180 |

If you observe the unit’s digit of the first 5 multiples of 6 – 6, 12, 18, 24, 30. You can see that as the list go on and on, the unit’s digit will just cycle around the numbers 6, 2, 8, 4, and 0.

Do you see any other pattern in the multiples of 6?

## Solving Problems

Now, let’s try to apply our knowledge in solving real-world situations.

### Problem #1

Shanaia is playing a board game called Snakes and Ladders. Each time she rolls the dice, she always gets a 6. How many steps did she already take on the board if she rolled the dice 18 times?

The problem states that every time Shaunaia rolls the dice, she always gets a 6. Hence, the problem is asking us to get the 18^{th} multiple of 6 to get the total number of steps she already took in the board game. Multiplying 6 by 18, we will have:

**6 x 18 = 108**.

Therefore, there Shanaia already made **108 steps** in Snakes and Ladders on her 18^{th} roll.

### Problem #2

Albie is arranging a bouquet in such a way that there are 6 flowers in the first one, 12 on the second, and 18 on the third, and so on. How many flowers does Albie need to make the 32^{nd} bouquet?

The given problem tells us that as Albie makes another bouquet, the number of flowers increases. If we find the difference between the first and second bouquet, we have **12 – 6 = 6**. More so, if we look at the difference between the third and second bouquet, the result will be **18 – 12 = 6**.

Consequently, to get the total number of flowers on the 32^{nd} set, we will multiply 6 by 32. Thus, **6 x 32 = 192**.

Therefore, Albie needs **192 flowers** to make the 32^{nd} bouquet.