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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.

A deficit is when you don't have enough of something to get what you want or for it to be complete. Did you know that numbers can be deficient? Read along in this lesson to find out about the numbers that just aren't quite complete.

It's important to eat a healthy diet of fruits, vegetables, protein, and dairy products to make sure you get all the nutrients and vitamins your body needs to grow strong. If you don't get enough of these vitamins from your diet, you may become deficient. When your body becomes deficient, it lacks the important nutrients you need to be healthy and strong. Did you know numbers can also be deficient? Let's learn what it means when a number is deficient.

**Deficient numbers** are numbers that don't have much value when broken down into a sum of its proper factors. For example, the proper factors of 8 are 1, 2, and 4. This is because a **proper factor** is any factor of a number except the number itself. So, 8 is just a factor of itself, it is not a *proper* factor of 8. Now, if I add the proper factors of 8 together, I will get another number. Right? If this new number is less than 8, then 8 is a deficient number. So let's add 1 + 2 + 4 = 7. The number 7 is less than 8. So, this means that 8 is a deficient number! Look at the image below which uses Cuisenaire rods to demonstrate just how the number 8 is deficient.

Let's figure out if the number 21 is a deficient number. Are you ready?!

1, 3, and 7

1 + 3 + 7 = 11

11 is less than 21. So, this means that 21 is a deficient number! Wow!

Now let's figure out if the number 36 is deficient.

1, 2, 3, 4, 6, 9, 12, and 18

1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 45

Now 45 is larger than 36. So, 36 is not a deficient number!

Deficient numbers are sometimes called defective numbers. It almost sounds as if they're broken! Did you know that all prime numbers are also deficient? The only proper factor of a prime number is 1, so they're automatically all deficient. There are far more deficient numbers than there are abundant numbers when counting up to 100. Abundant numbers are numbers whose sum of its proper factors is greater than the original number. Remember how the sum of the proper factors of 36 added to 45? So 45 is an abundant number!

**Deficient numbers** are numbers that aren't made up of what they're worth. To find out if a number is deficient, add the **proper factors** of a number and see if the sum is less than the original number. If the sum is less than the original number, than the number is deficient.

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7 in chapter 12 of the course:

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Math for Kids23 chapters | 325 lessons

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- What is an Abundant Number?
- What is a Base 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 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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