Abundant number facts for kids

An abundant number is a special kind of whole number. If you add up all the numbers that divide into it perfectly (these are called its divisors), the total will be more than double the original number!

For example, let's look at the number 12. The numbers that divide into 12 are 1, 2, 3, 4, 6, and 12. If we add them up: 1 + 2 + 3 + 4 + 6 + 12 = 28. Now, let's double 12: 2 × 12 = 24. Since 28 is greater than 24, 12 is an abundant number!

Another example is 18. Its divisors are 1, 2, 3, 6, 9, and 18. Adding them up: 1 + 2 + 3 + 6 + 9 + 18 = 39. Double 18 is 2 × 18 = 36. Since 39 is greater than 36, 18 is also an abundant number.

The first few abundant numbers are: 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72. You can find a list of these numbers in the Online Encyclopedia of Integer Sequences under the code A005101. The first odd abundant number is 945.

Finding Abundant Numbers

To find out if a number is abundant, you need to follow these steps:

• Step 1: List all the divisors of the number. Remember to include 1 and the number itself.
• Step 2: Add up all these divisors.
• Step 3: Double the original number.
• Step 4: Compare the sum of the divisors to the doubled number. If the sum is larger, then it's an abundant number!

Most abundant numbers are even numbers. Odd abundant numbers are much rarer. The smallest odd abundant number is 945.

List of Abundant Numbers

Here is a list of the first 90 abundant numbers:

Images for kids

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  Demonstration, with Cuisenaire rods, of the abundance of the number 12

See also

In Spanish: Número abundante para niños