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Math for Kids23 chapters | 325 lessons

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Instructor:
*Danielle Wilson*

Danielle is a certified elementary, middle school math, and special education teacher. She has a master's degree in elementary education and special education.

There are so many things we can do with numbers. We can add them, multiply them, find their square roots and much more. In this lesson, you will learn what an abundant number is and how to figure out if a number is abundant.

Could you imagine having an abundance of money? What would you buy? Would you go on a long beach vacation? Or would you buy all of the video games you've always wanted? When you have an abundance of something, it means you have a large amount. So then, what exactly is an abundant number?

An **abundant number** is a number where the sum of all its proper factors is larger than the original number. Abundant numbers are cool - you can think of them as being made up of more than what they're worth! Abundant numbers are a lot like U.S. pennies. It costs about 1.7 cents to make a single penny, but all pennies are only worth one cent! Hard to believe, right?

In order to determine if a number is abundant, you must first find all of the number's proper factors. While **factors** are numbers that you multiply together to get another number, **proper factors** are all the factors of the number *except* the number itself.

Once you have found all of the proper factors of a number, you add them together. If the sum of the proper factors is greater than your actual number, then the number is considered to be an abundant number.

The first abundant number is 12. The proper factors of 12 are 1, 2, 3, 4, and 6. Now that we have factored, let's add the factors together. If you add 1 + 2 + 3 + 4 + 6 you will get 16. The number 16 is greater than the number 12, so 12 is an abundant number. The difference between the sum of the factors and the original number is known as the **abundance**. The abundance of 12 is 4, because 16 - 12 = 4.

Is 24 an abundant number?

1, 2, 3, 4, 6, 8, 12

1 + 2 + 3 + 4 + 6 + 8 + 12 = 36

Since 36 is greater than 24, 24 is also an abundant number. 36 - 24 = 8 so the abundance of 24 is 8.

Okay, now I want you to grab a pencil and paper and figure out if 48 is abundant, and if it is, find the abundance.

Remember to first list the proper factors of the number! Be sure not to scroll down and peek at the answer.

Did you get your answer? Awesome! First we will list the proper factors of 48 and add them together:

1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 = 76

Wow! Look at that! 76 is greater than 48, so 48 must be an abundant number.

76 - 48 = 28, so the abundance of 48 is 28.

There are an infinite number of abundant numbers. The first 10 abundant numbers are 12, 18, 20, 24, 30, 36, 40, 42, 48, and 54. There are only a total of 21 abundant numbers under 100 and all of these numbers are even. The first odd abundant number is 945!

**Abundant numbers** are numbers that are made up of more than they're worth. You can find an abundant number by adding up the **proper factors** of a number to see if they add up to more than the number itself. The **abundance** of a number is the difference between the sum of the proper factors and the number. Identifying number abundance is helpful in making sense of the numbers we use in mathematics. Abundant numbers can be fun and test your math skills at the same time!

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Math for Kids23 chapters | 325 lessons

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- What is an Abundant Number?
- What Are Cardinal Numbers? - Definition & Examples 3:06
- What Are Consecutive Numbers? - Definition & Examples 3:22
- Finding the Sum of Consecutive Numbers 4:10
- What is a Cubed Number?
- What is a Deficient Number?
- What Are Figurate Numbers? - Definition & Examples
- What Are Opposite Numbers? - Definition & Examples 2:53
- What Are Rectangular Numbers? - Definition & Examples 3:05
- Like & Unlike Terms
- Is Zero an Integer?
- Is Zero a Natural Number? 2:37
- Sieve of Eratosthenes: Lesson for Kids
- What Are Twin Prime Numbers? 3:22
- Go to Types of Numbers for Elementary School

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