kids encyclopedia robot

Abundant number facts for kids

Kids Encyclopedia Facts

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:

12 18 20 24 30 36 40 42 48 54
56 60 66 72 78 80 84 88 90 96
100 102 104 108 112 114 120 126 132 138
140 144 150 156 160 162 168 174 176 180
186 192 196 198 200 204 208 210 216 220
222 224 228 234 240 246 252 258 260 264
270 272 276 280 282 288 294 300 304 306
308 312 318 320 324 330 336 340 342 348
350 352 354 360 364 366 368 372 378 380

Images for kids

See also

Kids robot.svg In Spanish: Número abundante para niños

kids search engine
Abundant number Facts for Kids. Kiddle Encyclopedia.