# What Are Composite Numbers?

What are composite numbers? Whether you’re teaching upper elementary math for the first time or the first time in a while, you may need a refresher on this core concept. Often learned along with prime numbers, a composite number is a whole number or natural number that has more than two factors.

What are some examples of composite numbers? And how do composite numbers differ from prime numbers? Let’s take a look at tips on how to explain this math concept to your students.

## What Are Composite Numbers?

The word “composite” comes from the Latin word compositum meaning “put together.” With this in mind, it makes sense that composite numbers are made up of things that are “put together” — its factors.

But wait, what’s a factor? A factor is a number or algebraic expression that divides another number or expression evenly. For example, both 2 and 5 are factors of 10 because 10÷2 = 5 with nothing left over, and 10÷5 = 2 with no remainder. A factor is a type of divisor — a word that refers to any number that divides another number — but a number only counts as a factor if it can divide another number evenly.

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#### Factor Trees – Worksheet

A worksheet with factor trees that are used to find the prime factors of numbers. 4 pagesGrades: 5 - 6

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#### Math Mazes – Factors

A set of math mazes that allow students to demonstrate their knowledge of factors. 6 pagesGrades: 5 - 6

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#### Find a Factor

Strengthen multiplication and mental math skills with this factor game. 3 pagesGrades: 3 - 4

Composite numbers are all whole, which means that they do not have fractions. They are also integers, which is another word for whole numbers. Finally, composite numbers are always positive numbers, not negative numbers.

## Examples of Composite Numbers

Any number that is divisible by itself, 1, and another number is considered a composite number. The smallest composite numbers that students will encounter are 4, 6, 8, and 9 — each of which has at least three factors.

• Four, for example, is divisible by 1, 2, and 4.
• Six is divisible by 1, 2, 3, and 6.

The smallest composite number you will find is 4. Students can figure out the smallest composite numbers simply by starting from 1 and counting until they find the first number that is divisible by at least 3 whole numbers.

## Composite Numbers vs. Prime Numbers

Are all numbers composite numbers? Nope! Whole numbers can either be composite or prime.

Prime numbers are numbers greater than 1 that can only be divided evenly by itself and the number 1. That means they have just two factors. That sets them apart from composite numbers, which of course can be divided evenly by at least three numbers.  For example, 3 is a prime number because the only divisors that don’t leave a remainder are 1 and 3. The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

On the other hand, 60 is a composite number. It can be divided evenly by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. That makes 60 a great example of a composite number. Meanwhile, 59 and 61 are examples of prime numbers as they can only be divided by 1 and themselves.

There is only one even prime number — 2 — which can be divided evenly by 2 and 1.

But there are a number of odd composite numbers! For example, 9 is a composite number that can be divided evenly by 1, 3, and 9. Another odd composite number is 15 which can be divided by 1, 3, 5, and 15  evenly without anything left over.

## What Are the Properties of Composite Numbers?

Here are the properties to keep in mind when you are teaching what a composite number is and isn’t:

• Composite numbers are positive integers, never negative numbers.
• Composite numbers are created by multiplying two smaller positive integers.
• Composite numbers are evenly divisible by at least three smaller numbers.
• Composite numbers can be divided by prime or composite numbers.
• Composite numbers are made up of two or more prime numbers.

## Composite Number Activities

Help your students spot composite numbers and differentiate them from prime numbers with these teacher-created activities for math class:

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#### Prime and Composite Number Sort

Identify prime and composite numbers by sorting 30 number cards into their proper category. 7 pagesGrades: 4 - 5

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#### Prime and Composite Numbers Worksheet

A worksheet to practice the relationship between factors and prime and composite numbers. 2 pagesGrades: 4 - 5

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#### Find and Color: Prime and Composite Numbers Worksheet

A find and color worksheet to practice identifying prime and composite numbers up to 100. 2 pagesGrades: 4 - 5