# Multiples – Definition with Examples

9 minutes read

Created: January 7, 2024

Last updated: January 7, 2024

Hello budding mathematicians and inquisitive minds! Welcome to another exciting journey through the captivating universe of numbers with Brighterly. Today, we are going to explore the concept of multiples. Just as a rainbow has multiple colors, numbers too have multiples! Let’s dive into this world where numbers play the melody and multiples set the rhythm. Hold on to your curiosity as we journey into the realm of multiples, a fundamental concept in mathematics that allows us to understand and appreciate the harmony and patterns inherent in the world of numbers. You’ll find multiples popping up everywhere, from the steps you climb to the coins in your pocket. So let’s get started and uncover the magic that multiples hold!

## What is a Multiple?

Have you ever wondered what happens when you multiply a number by another? You get what mathematicians call a multiple. Picture multiples as the colorful blooms of a plant, where each bloom is a result of the multiplication operation. Just as a plant grows and sprouts more flowers, the multiplication operation sprouts multiples. For instance, if we take the number 2 and start multiplying it by integers, we get multiples of 2 like 2, 4, 6, 8, and so forth. Each of these numbers is a unique bloom sprouted from the seed of 2!

## What is a Multiple of a Number?

The phrase “multiple of a number” refers to the fascinating array of products that emerge when we multiply that number by any integer, including zero. Just as a tree grows branches, the number grows multiples. So, if we take a number, say 3, and multiply it by different integers, we get its multiples: 0, 3, 6, 9, 12, and so on. Each of these multiples is like a new branch sprouting from the trunk of the number 3!

## Properties of Multiples of a Number

The world of multiples is filled with intriguing properties and patterns! One of the most interesting properties is that every number is a multiple of itself. Just as you are unique to yourself, each number is a multiple of itself, because when you multiply a number by 1, you get the number itself. The smallest multiple of any number is the number itself. Also, zero, the magical number in mathematics, is a multiple of every number because any number multiplied by 0 equals 0. Zero is like the universal shadow of all numbers in the realm of multiples!

## Factors and Multiples

Factors and multiples are the yin and yang of mathematics; two sides of the same coin with different roles. A factor is a number that divides another number without leaving any leftover crumbs – it fits perfectly like a piece in a puzzle. A multiple, on the other hand, is what we get when we multiply a number by an integer. It’s like creating a tower of blocks where each block is a factor. For instance, 1, 2, and 4 are the building blocks (factors) of 4, while the towers you can make with these blocks (4, 8, 12) are multiples of 4.

## Common Multiples

Just as friends have common interests, numbers have common multiples. These are multiples that two or more numbers share. It’s like finding a meeting point for different number lines. For example, if we take the numbers 12 and 18, they both meet at the common multiples of 36, 72, 108, and so on. It’s like a party where both 12 and 18 are invited!

## How to Find the Multiple of a Number

Finding the multiple of a number is like embarking on a treasure hunt. The map is the number, the treasures are the multiples, and your tool is multiplication. To find the multiples of a number, you simply start multiplying that number by different integers. For example, to find the treasures (multiples) of 5, you start multiplying 5 by 1, 2, 3, 4, and so on. Each product you find is a discovered treasure – a multiple of 5!

You can explore more about multiples and apply your newfound knowledge through our Multiples Worksheet available on Brighterly. This resource provides a wealth of practice questions and detailed solutions to help solidify your understanding of multiples in mathematics. Happy learning!

## What is a Multiple of 2

Multiples of 2 are all the even numbers we encounter daily: 2, 4, 6, 8, 10, and so on.

## What is a Multiple of 3

Multiples of 3 are numbers like 3, 6, 9, 12, 15, and so on. Notice that every third number in the sequence of natural numbers is a multiple of 3.

## What is a Multiple of 4

Multiples of 4 include numbers such as 4, 8, 12, 16, 20, and so forth.

## What is a Multiple of 5

Multiples of 5 end with a 0 or 5, like 5, 10, 15, 20, and so on.

## What is a Multiple of 6

Multiples of 6 can be found by doubling the multiples of 3: 6, 12, 18, 24, and so forth.

## What are the Multiples of 8

The multiples of 8 are numbers like 8, 16, 24, 32, and so on.

## What is a Multiple of 10

The multiples of 10 make up the tens in our decimal number system: 10, 20, 30, 40, etc.

## Multiples Examples

Let’s illustrate with some examples:

- Multiples of 7: 7, 14, 21, 28, 35, and so on.
- Multiples of 9: 9, 18, 27, 36, 45, and so on.

## Practice Questions on Multiples

Now it’s your turn to practice. Here are some questions for you:

- What are the first five multiples of 11?
- What are the first five multiples of 15?
- Find the common multiples of 4 and 6.

## Conclusion

Congratulations! You’ve journeyed through the dynamic world of multiples with us today. Understanding multiples is like learning the choreography of mathematics. They dance through algebra, twirl around fractions, and leap into number theory. With multiples, you’ve not only learned a concept, but you’ve gained a key that opens many doors in the world of mathematics. But remember, every great mathematician started exactly where you are now. There’s no end to learning, and there’s always more to explore.

At Brighterly, we believe that every child is capable of understanding complex concepts when they are explained in a fun and engaging way. We’re here to make math less daunting and more exciting. So keep learning, keep exploring, and keep growing. The world of multiples is just one stop on your journey through the universe of mathematics. There’s so much more to discover. Stay curious, keep practicing, and soon, you’ll not just master the concept of multiples, but you’ll embrace the rhythm of numbers and dance to the melody of mathematics. Until next time, keep your spirit of exploration alive with Brighterly!

## Frequently Asked Questions on Multiples

### What is the difference between a multiple and a factor?

In the world of numbers, multiples and factors are like best friends that have unique roles. A multiple is like an enthusiastic storyteller, expanding and growing as it recounts its tale. When you multiply a number by any integer, you get a multiple. For instance, if you multiply 5 by any number, you get multiples of 5 (like 5, 10, 15, 20, and so forth).

A factor, on the other hand, is like a careful investigator, breaking numbers down into smaller parts. Factors are numbers that neatly divide another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers can divide 12 without leaving any pieces behind. So, while a multiple grows the story of a number, a factor simplifies it, breaking it down to its essentials!

### Is zero a multiple of every number?

Absolutely! Zero is indeed a multiple of every number. Think of zero as the great equalizer in the number family. Regardless of which number you choose, if you multiply it by zero, the answer will always be zero. This makes zero a multiple of all numbers. It’s a neat trick that zero has up its sleeve!

### Are all numbers multiples of 1?

Yes, indeed! Every number is a multiple of 1, making 1 a sort of universal multiplier. This is because multiplication by 1 has a unique property: any number times 1 equals the original number. So whether you have a huge number like 10,000 or a small number like 0.01, multiplying by 1 keeps them exactly the same. In other words, every number dances to its own tune, and 1 is the perfect dance partner that lets them shine!

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