Composite number facts for kids

See how the number 10 can be made from smaller blocks (2 and 5)? That makes it a composite number!

A composite number is a whole number that is greater than 1 and can be divided evenly by numbers other than 1 and itself. Imagine you have a certain number of items. If you can arrange them into a rectangle (not just a single line) using smaller groups, then that number is composite.

For example, the number 14 is a composite number. You can make 14 by multiplying 2 and 7 (2 × 7 = 14). So, 14 can be divided by 2 and 7, as well as 1 and 14. On the other hand, numbers like 2 and 3 are not composite. They can only be divided evenly by 1 and themselves. Numbers that are not composite (and not 1) are called prime numbers.

What are Some Composite Numbers?

The smallest composite number is 4. You can get 4 by multiplying 2 × 2. Other composite numbers include:

• 6 (2 × 3)
• 8 (2 × 4)
• 9 (3 × 3)
• 10 (2 × 5)
• 12 (3 × 4 or 2 × 6)

Here are some composite numbers up to 50: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50. You can find a much longer list of composite numbers in the Online Encyclopedia of Integer Sequences ((sequence A002808 in OEIS)).

Breaking Down Composite Numbers

Every composite number can be broken down into a unique set of prime numbers. This is like saying every building block structure can be taken apart into its basic, un-breakable blocks. This important idea is called the fundamental theorem of arithmetic.

Let's look at some examples:

• The composite number 299 can be written as 13 × 23. Both 13 and 23 are prime numbers.
• The composite number 360 can be written as 2 × 2 × 2 × 3 × 3 × 5. This can also be written using powers: 2³ × 3² × 5. No matter how you start to break down 360, you will always end up with these same prime factors.

How Do We Know if a Number is Composite?

Mathematicians use special methods called primality tests to figure out if a very large number is prime or composite. These tests can tell you if a number is composite without actually finding all of its smaller factors. It's like knowing a building is made of many blocks without having to count every single one!

Other pages

• Perfect number

See also

In Spanish: Número compuesto para niños