# Multiples of 30

**Time** is the seemingly irreversible continuity of existence and events that occur from the past, through the present, and into the future – and the number **thirty** is closely related to how we measure time. We measure time by seconds, minutes, hours, weeks, months, or even years.

But what makes 30 a significant number in measuring time because half a second is 30, half a minute is 30 seconds, half an hour is 30 minutes, and even the average number of days in a month is **thirty**.

Now, are you ready to allot this time to learn more about the beautiful facts of 30? Fasten your seats as we take off to another journey of finding multiples!

## Multiples of 30 are 30, 60, 90, 120, 150 …

When a random number is multiplied by thirty, the result is a multiple of thirty. Multiples of 30 are numbers where if you divide it by 30, it will always have a **zero remainder**. So, numbers such as 30, 60, 90, 120, 150… and so on are multiples of 30.

But, can negative numbers be a multiple of 30? Definitely! Since there are negative integers like -1, -2, -3, -4, -5… and so on, we can multiply it by 30, giving us negative multiples of 30.

We need to remember that we cannot multiply fractions to 30 since we aim to get numbers that when divided by 30, we will have a **whole number**.

## How to find the multiples of 30?

Knowing the definition of multiples of 30 will help us better understand finding its possible multiples. There are two ways to generate multiples of 30 – by **repeated addition** or by **multiplication**.

**Repeated addition** or **skip counting** is one of the methods we use the find any multiples of 30. So how do we do it? This process is done by simply repeatedly adding 30. So, we start by 0 and add 30 to get the first positive multiple of 30.

Hence, **0 + 30 = 30**.

Now that we know the first multiple of 30, to get its 2^{nd} multiple, we continue adding 30 to it. Thus, **30 + 30 = 60**. Therefore, the 2nd multiple of 30 is 60.

It’s so simple, right? Now, can you try finding the 6th multiple of 30 by repeated addition?

So, **30 + 30 + 30 + 30 + 30 + 30 = 180**.

It’s fun repeatedly adding numbers, isn’t it? But will it still be fun if we are asked to get the 500^{th} multiple of 30 or even the 100^{th} multiple of 30? Using repeated addition only works if we are looking for the 10^{th} or even up to the 20^{th} multiple of 30.

However, using this process can be time-consuming. Hence, the need to learn the second method – which is **multiplication**!

We have already defined multiples that it is a product of 30 and an integer. So, we can denote any multiples of 30 as **30 n** where

*n*is an integer.

Say, we are asked to get the 15^{th} multiple of 30. Using multiplication method, we can easily find its multiple by simply multiplying 30 by 15. Hence, $$30\;\times\;15\;=\;450$$. Therefore, the 15^{th} multiple of 30 is 450.

How about the 75^{th} multiple of 30? Using the same method, the 75^{th} multiple of 30 is the result of getting the product of 30 and 75. So, $$30\;\times\;75\;=\;2250$$.

Integers can be positive – but can also be negative! So, multiples can also be negative. Now, if we want to find the 16^{th} multiple of 30, we simply multiply 30 by -16. Hence, $$30\;\times\;-16\;=\;-480$$. Therefore, the 16th negative multiple of 30 is -480.

Now, let’s take a look at this table. This summarizes the two methods in determining multiples of 30 and how they differ with each other.

n^{th} Multiple | Repeated Addition | Multiplication |
---|---|---|

1^{st} multiple | 30 | $$30\;\times\;1\;=\;30$$ |

2^{nd} multiple | 30 + 30 = 60 | $$30\;\times\;2\;=\;60$$ |

3^{rd} multiple | 30 + 30 + 30 = 90 | $$30\;\times\;3\;=\;90$$ |

4^{th} multiple | 30 + 30 + 30 +30 = 120 | $$30\;\times\;4\;=\;120$$ |

5^{th} multiple | 30 + 30 + 30 + 30 + 30 = 150 | $$30\;\times\;5\;=\;150$$ |

## List of First 30 multiples of 30

There are infinitely many positive and negative numbers. Hence, listing all the possible multiples of 30 makes no sense. However, you can see the list of the first 30 multiples of 30 that is generated by multiplying 30 by numbers 1 – 30.

Product of 30 and a positive counting number | Multiples of 30 |
---|---|

$$30\;\times\;1$$ | 30 |

$$30\;\times\;2$$ | 60 |

$$30\;\times\;3$$ | 90 |

$$30\;\times\;4$$ | 120 |

$$30\;\times\;5$$ | 150 |

$$30\;\times\;6$$ | 180 |

$$30\;\times\;7$$ | 210 |

$$30\;\times\;8$$ | 240 |

$$30\;\times\;9$$ | 270 |

$$30\;\times\;10$$ | 300 |

$$30\;\times\;11$$ | 330 |

$$30\;\times\;12$$ | 360 |

$$30\;\times\;13$$ | 390 |

$$30\;\times\;14$$ | 420 |

$$30\;\times\;15$$ | 450 |

$$30\;\times\;16$$ | 480 |

$$30\;\times\;17$$ | 510 |

$$30\;\times\;18$$ | 540 |

$$30\;\times\;19$$ | 570 |

$$30\;\times\;20$$ | 600 |

$$30\;\times\;21$$ | 630 |

$$30\;\times\;22$$ | 660 |

$$30\;\times\;23$$ | 690 |

$$30\;\times\;24$$ | 720 |

$$30\;\times\;25$$ | 750 |

$$30\;\times\;26$$ | 780 |

$$30\;\times\;27$$ | 810 |

$$30\;\times\;28$$ | 840 |

$$30\;\times\;29$$ | 870 |

$$30\;\times\;30$$ | 900 |

## Did you know that…

…if a number is divisible by 5 and 6, we can already conclude that it is a multiple of 30?

Let’s try if this is true.

Consider the number 120.

To say that a number is divisible by 5, it should either end at 0 or 5. The given number ends at 0, so it is divisible by 5.

Now, let’s see if it is divisible by 6.

If a number is divisible by 6, it should be a multiple of 2 and 3.

So, to say that a number is divisible by 2, it should be an even number. 120 is an even number because it ends at 0.

Lastly, we need to check if the sum of the digits of 120 is divisible by 3. So, 1 + 2 + 0 = 3. 3 is divisible by 3.

Since 120 is divisible by 5 and 6. We can therefore conclude that 120 is a multiple of 30.

So, if we are asked to determine if a number is a multiple of 30, we can easily do this by checking if:

- it is an even number.
- a multiple of 5; and
- the sum of all its digits is divisible by 3.

Now, let’s try if 784620 is a multiple of 30 using this technique.

Is it an even number? Yes.

Is it a multiple of 5? Yes.

Is the sum of the digits of 784620 a multiple of 3? Adding the digits 7 + 8 + 4 + 6 + 2 + 0 = 27.

Since 27 is divisible by 3, we can say that 784620 is also a multiple of 3.

Therefore, 784620 is definitely a multiple of 30!

What a trick, right? Makes it easy for us to check if a number is a multiple of 30!

## Solving problems involving multiples of 30

Now, let’s try to solve problems that we may encounter in our daily lives.

### Problem #1

Jennie works 30 hours a week as a freelance writer at a rate of $30/hour. How much does Jennie earn in a week? How about in a month?

In this problem, we are asked to find the weekly and monthly earnings of Jennie. What we know so far is that she earns $30 per hour. So, to get her weekly salary, we need to multiply it by the total number of hours she works in a week.

Since she works 30 hours each week, we need to get the 30th multiple of 30. Hence,

$$\$30\;\times\;30\;=\;\$900$$.

Thus, Jennie earns $900 a week. Now, we need to know her monthly salary.

There are 4 weeks in a month. So, to solve for Jennie’s monthly salary, we need to multiply Jennie’s weekly salary by 4. Thus,

$$\$900\;\times\;4\;=\;\$3600$$.

Therefore, Jennie’s weekly earning is $900, while her monthly salary is $3600!

Isn’t it fun solving problems we can use in our daily lives? Now, let’s try another one.

### Problem #2

Jisoo saves her money to buy a vlogging camera that costs $540. If she saves $30 a week, how many weeks will it take her to buy the camera?

In the given problem, Jisoo needs to save $540 to be able to buy a camera. Our task is to find the number of weeks it will take her if she saves $30 a week. Hence, we need to divide $540 by $30. Thus, $540 ÷ $30 = 18 weeks.

Therefore, Jisoo needs to save $30 for 18 weeks to buy the camera.