# Multiples of 60

The Babylonians’ contributed a lot to our number system – and one of which is probably the number sixty. Without the Babylonians, we wouldn’t have known the number of seconds in a minute – or even the number of minutes in an hour. Sixty is an ancient and mysterious yet exciting number.

While it is indeed a historical number, the number 60 has so much to offer – and that is on our agenda for today! Let’s take a quick drive to and learn more about this number and its multiples!

## Multiples of 60 are 60, 120, 180, 240 …

Multiples of 60 are numbers that can be expressed as a product of 60 and any integer. Hence, if a number is multiplied by 60, we can easily consider it as a multiple of 60.

So, if a sequence of numbers has a difference of 60 between two consecutive numbers, it means they are multiples. However, that is not always the case.

Let’s consider these two sequence of numbers:

*-60, 0, 60, 120, 180, 240 and 66, 126, 186, 246*

The difference between two consecutive numbers of the two sequences is 60. However, if we divide 66 by 60, we will get a remainder of 6. Hence, we cannot consider that sequence as multiples of 60.

So, to get the whole concept of multiples of 60, we only need to remember these things:

- It should always have a zero remainder when divided by 60;
- We cannot use fractions to generate multiples of 60.

Now, I guess we are ready to learn how to determine any possible multiples of 60, aren’t we?

## How to find the multiples of 60?

Now, finding multiples of 60 is almost the same as finding multiples of 6 and 10. So, in this case, if you have already mastered the art of generating any multiples of 6, this will just be a piece of cake – since we can easily add 0 to all multiples of 6 and say that it is a multiple of 60.

But for starters, we’ll teach you the two basic methods we can use – repeated counting and multiplication!

As the name suggests, repeated counting is to repeatedly add 60 as many times as we want depending on the nth multiple we are looking for. Say, we are looking for the 1st multiple of 60, we simply add 0 and 60 to get its first multiple. Hence, 0 + 60 = 60. Therefore, the first multiple of 60 is the number itself. So, if we continue this process until the 5th multiple, we will have the result same as the diagram.

Now, if we are asked to get the 7th multiple of 60, we will simply add 60 seven times. Hence, **60 + 60 + 60 + 60 + 60 + 60 + 60 = 420**.

While it is indeed fun and easy to repeatedly add numbers, this will take us so much time if we are asked to get the 100th or even the 50th multiple of 60 using this method. That’s why we have another way called **multiplication!**

We have defined multiples as a product of two numbers. So, if a number is expressed as **60 n, where n is an integer, we can easily say that it is a multiple of 60.**

So, if we are asked to get the 67th multiple of 60, we will simply multiply 60 by 67. Thus, **60 x 67 = 4,020**. Therefore, the 67th multiple of 60 is 4,020.

…but wait! Multiples of 60 can also be negative since we can multiply negative integers to 60. Say, we are looking for the negative 23rd multiple of 60, we will simply multiply 60 by -23. Hence, **60 x -23 = -1,380**. Therefore, the negative 23rd multiple of 60 is -1,380!

Determining any possible multiples of 60 are very simple, right?

Let’s take a look at this table. This shows the two methods that we can use in generating multiples of 60, which method do you prefer to use?

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

1^{st} multiple | 60 | 60 x 1 = 60 |

2^{nd} multiple | 60 + 60 = 120 | 60 x 2 = 120 |

3^{rd} multiple | 60 + 60 + 60 = 180 | 60 x 3 = 180 |

4^{th} multiple | 60 + 60 + 60 + 60 = 240 | 60 x 4 = 240 |

5^{th} multiple | 60 + 60 + 60 + 60 + 60 = 300 | 60 x 5 = 300 |

## Did you know that…

…the speed limit of some countries is 60 kilometers per hour?

## List of First 30 multiples of 60

We cannot really list all the possible multiples of 60 because infinitely many integers exist. Hence, giving us infinite possibilities to generate multiples of 60. In this section, we have listed the first 30 multiples of 60 that can be generated by multiplying 60 from numbers 1 – 30. This table will help us verify and practice what we know about multiples.

Product of 60 and a positive counting number | Multiples of 60 |
---|---|

60 x 1 | 60 |

60 x 2 | 120 |

60 x 3 | 180 |

60 x 4 | 240 |

60 x 5 | 300 |

60 x 6 | 360 |

60 x 7 | 420 |

60 x 8 | 480 |

60 x 9 | 540 |

60 x 10 | 600 |

60 x 11 | 660 |

60 x 12 | 720 |

60 x 13 | 780 |

60 x 14 | 840 |

60 x 15 | 900 |

60 x 16 | 960 |

60 x 17 | 1020 |

60 x 18 | 1080 |

60 x 19 | 1140 |

60 x 20 | 1200 |

60 x 21 | 1260 |

60 x 22 | 1320 |

60 x 23 | 1380 |

60 x 24 | 1440 |

60 x 25 | 1500 |

60 x 26 | 1560 |

60 x 27 | 1620 |

60 x 28 | 1680 |

60 x 29 | 1740 |

60 x 30 | 1800 |

## Problem #1

Kirsten is doing a donation drive to buy school supplies for orphan kids. Her target budget for each kid is $60. If she has collected a total amount of $5400, how many kids will receive a set of school supplies?

In this given problem, we are asked to determine the total number of kids who will receive the donated school supplies. We know that Kirsten has collected $5400 from donations and targets $60 for each kid. So, in order to get the total number of kids that will receive a set of school supplies, we need to divide the total collected money to the cost of a set of school supplies. Hence, **$5400 ÷ $60 = 90.**

Therefore, Kirsten will be able to give 90 sets of school supplies to orphan kids.

## Problem #2

Every time Elsa studies, she always sees to it that she takes an hour break. How many minutes did Elsa rest if she took a 3-hour break in an 8-hour study session?

The problem states that Elsa always takes an hour break every time she studies. We know that she took a 3-hour break, and we are asked to get the total number of minutes Elsa took a rest. So, for us to get the total number of minutes she takes a break, we need to convert the 3-hour break to minutes.

Since there are 60 minutes in an hour, we simply need to multiply 3 hours to 60 minutes. Hence, **3 x 60 = 180**

Therefore, Elsa took a 180-minute break while studying.