# Multiples of 25

Twenty-five is an **odd number** that is between twenty-four and twenty-six. It is the square of 5 and is also the **fifth square number** after 1, 4, 9, and 16. What’s cool about this number is that adding the squares of 3 and 4 will give us the square of 5! Does this excite you already?

Well… come and let’s take this journey to travel the world of 25 and find its multiples!

## Multiples of 25 are 25, 75, 75, 100, 125 …

A **multiple** is defined as the product of a number with any integer. So, if we say that a number is a multiple of 25, it means that it is a result of **multiplying 25 to any integer**. More so, if we divide a random number by 25, we should always get a **whole number**. Yes, you read that right! We cannot have a remainder if we are talking about multiples!

The numbers -75, -50, -25, 0, 25, 50, 75 are some of the multiples of 25.

Now, let’s take a look at these numbers! Can you spot what number or numbers is not a multiple of 25?

50, 75, 100, 125, 145, 175, 180

Correct! 145 and 180 are not multiples of 25… but can you tell us why?

If we divide 145 by 25, we will get a result of 5 with a remainder of 20. Likewise, dividing 180 by 25 will give us a quotient of 7 with a remainder of 5.

It’s so simple to understand the meaning of multiples, right? Now, let’s take this adventure a little further and find out how we can generate any multiples of 25! Are you ready?

## How to find the multiples of 25?

We have already defined what a multiple of 25 is. Now, our next task is to determine any possible multiple of 25. We have two ways to determine any multiple of 25, and that is by doing the **repeated addition** and **multiplication**.

**Skip counting** or **repeated addition** is a method where we start from 0 and add 25 as many times as possible. So, if we add 25 to 0, we will have the first positive multiple of 25 – which is the number itself.

Since 25 is the first multiple of 25. Then, to get the 2nd multiple, all we need to do is add another 25. Hence, **25 + 25 = 50**. Therefore, the 2^{nd} multiple of 25 is 50.

Did you get it? Now, let’s try to get the 4^{th} multiple of 25 by repeated addition.

So, **25 + 25 + 25 + 25 = 100**.

Getting multiples of 25 using repeated addition is so easy, right? But what if we need to find the 100^{th} or the 1056^{th} multiple of 25? Can we still use the same method we are using?

Well… we can still use repeated addition, but it will take some time before we can finally arrive at a final answer. That’s why we have another method called **multiplication**!

By definition, we say that a multiple of 25 is a product of a 25 and any integer. Hence, we can mathematically express it as * 25n* where

*n*is an integer.

So, if we are asked to get the 105^{th} multiple of 25, we can easily find the answer using multiplication method.

Hence, **25 x 105 = 2625**. Therefore, the 105^{th} multiple of 25 is 2625.

But wait, there’s more… integers can also be negative! This means that multiples of 25 can also be a negative number. So, can you help me determine the 34^{th} negative multiple of 25?

By multiplication method, we will simply multiply 25 by -34. Hence, **25 x -34 = -850**. Therefore, the 34th negative multiple of 25 is **-850**.

So let’s recap a little. Skip counting and multiplication are the two methods we can use to determine and generate any multiples of 25. Let’s take a quick look on this table below.

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

1^{st} multiple | 25 | $$25\;\times\;1\;=\;25$$ |

2^{nd} multiple | 25 + 25 = 50 | $$25\;\times\;2\;=\;50$$ |

3^{rd} multiple | 25 + 25 + 25 = 75 | $$25\;\times\;3\;=\;75$$ |

4^{th} multiple | 25 + 25 + 25 + 25 = 100 | $$25\;\times\;4\;=\;100$$ |

5^{th} multiple | 25 + 25 + 25 + 25 + 25 = 125 | $$25\;\times\;5\;=\;125$$ |

Finding multiples of 25 is such a piece of cake, isn’t it?

## List of First 30 multiples of 25

It is not logical to list all the possible multiples of 25 because this would result in infinitely many multiples of 25 – since there are infinitely many integers! This is why the table below only shows the first 30 multiples of 25 which is generated by multiplying 25 from numbers 1 to 30.

Product of 25 and a positive counting number | Multiples of 25 |
---|---|

$$25\;\times\;1$$ | 25 |

$$25\;\times\;2$$ | 50 |

$$25\;\times\;3$$ | 75 |

$$25\;\times\;4$$ | 100 |

$$25\;\times\;5$$ | 125 |

$$25\;\times\;6$$ | 150 |

$$25\;\times\;7$$ | 175 |

$$25\;\times\;8$$ | 200 |

$$25\;\times\;9$$ | 225 |

$$25\;\times\;10$$ | 250 |

$$25\;\times\;11$$ | 275 |

$$25\;\times\;12$$ | 300 |

$$25\;\times\;13$$ | 325 |

$$25\;\times\;14$$ | 350 |

$$25\;\times\;15$$ | 375 |

$$25\;\times\;16$$ | 400 |

$$25\;\times\;17$$ | 425 |

$$25\;\times\;18$$ | 450 |

$$25\;\times\;19$$ | 475 |

$$25\;\times\;20$$ | 500 |

$$25\;\times\;21$$ | 525 |

$$25\;\times\;22$$ | 550 |

$$25\;\times\;23$$ | 575 |

$$25\;\times\;24$$ | 600 |

$$25\;\times\;25$$ | 625 |

$$25\;\times\;26$$ | 650 |

$$25\;\times\;27$$ | 675 |

$$25\;\times\;28$$ | 700 |

$$25\;\times\;29$$ | 725 |

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

## Did you know that…

There is a very simple way on how we can easily determine if a big number is a multiple of 25 or not?

Suppose we have the numbers 5675, 5695, and 5685. Among these three numbers, only one of it is a multiple of 25.

The trick is simple, observe the last two digits of the multiples of 25. We can see that multiples of 25 end with either **0**, **25**, **50**, or **75**. Hence, to say that a large number is a multiple of 25, we need to** look at its last two digits!** Therefore, the only multiple of 25 from 5675, 5695, and 5685 is **5675**!

Isn’t it amazing?

Now, can you tell me which of these numbers is a multiple of 25?

675675, 600845, 678925, 600895, 643050

## Solving problems involving multiples of 25

Now, let’s put all that learning into some real-life application by working on these problems!

### Problem #1

Olive makes 25 different kinds of desserts. Every day, she distributes about 3750 desserts to different convenience stores. How many sets of 25 different desserts did Olive make?

So, it was stated that Olive distributes about 3750 desserts to different stores. Since we need to find out how many sets of 25 she made from 3750 desserts, we need to divide 25 from 3750. Hence, $$3750\;\div\;25\;=\;150$$.

Therefore, Olive was able to make **150 sets of 25 different desserts** in a day!

### Problem #2

Sammy collects $25 stamps. If her collection of $25 stamps is already valued at $1625. How many stamps does Sammy have?

To find the total number of $25 stamps Sammy has, we need to divide $1625 by $25. But why division and not multiplication?

Since the problem states that the total value of $25 stamps Sammy has is $1625, it means there **is ___ number of $25 stamps in $1625**. So, **$1625 ÷ $25 = 65.**

Thus, Sammy has 65-$25 stamps. That’s a lot of expensive stamps, but whatever that makes her happy!