Prime and composite numbers

##Let's review factors

Factors are whole numbers that can be divided evenly into another number.

$1, 3, 5,$ and $15$ are factors of $15$ because they can all be divided into $15$ without a remainder.

$15 \div 1 = 15$
$15 \div 3 = 5$
$15 \div 5 = 3$
$15 \div 15 = 1$

$15$ has four factors: $1, 3, 5$, and $15$.

[[☃ graded-group-set 1]]

All numbers have $\greenD{1}$ and $\purpleD{\text{themselves}}$ as factors.

$3 \div \greenD{1} = 3$
$3 \div \purpleD{3} = 1 $

Categories of numbers

We can divide almost all numbers into two categories: prime numbers and composite numbers.

###Prime numbers

Prime numbers are numbers with exactly $2$ factors.

A prime number's only factors are $\greenD1$ and the number $\purpleD{\text{itself}}$.

$7$ is an example of a prime number. Its only factors are $\greenD1$ and $\purpleD7$. It is not evenly divisible by any other whole numbers.

Let's use pictures to visualize prime numbers.

Farmer Maxwell is making a chicken coop for his best egg laying hens. He has $7$ hens and is thinking about how he can arrange them. He wants to arrange the hens in equal sized groups.

The only possibility is to make $1$ row of $7$ hens.
[[☃ image 1]]

Any other arrangements would not have the same number of hens in each row.

When there is only one possible way to divide a number into equal sized groups, that number is prime.

[[☃ graded-group-set 2]]

Composite numbers

Composite numbers have more than $2$ factors.

$16$ is an example of a composite number. The factors of $16$ are $1, 2, 4, 8$ and $16.$ All of these numbers divide into $16$ evenly.

Let's use pictures to visualize composite numbers.

Farmer Maxwell is also inventing a new egg carton where he will store the eggs his hens lay. He wants each carton to hold $16$ eggs.

He could have $1$ row of $16$ eggs.

[[☃ image 2]]

He could also have $2$ rows with $8$ eggs in each row.

[[☃ image 3]]

Or he could have $4$ rows with $4$ eggs in each row.

[[☃ image 4]]

Composite numbers have more than one way that they can be divided into equal groups.

[[☃ graded-group-set 1]]

###The number $1$

$1$ does not fit into either category. It is neither prime nor composite.

[[☃ explanation 7]]

##Practice with prime and composite numbers

[[☃ graded-group-set 1]]

##Prime number and composite number challenge

Use the clues given to solve the problems below.

[[☃ graded-group-set 1]]

##What are prime numbers?

Prime numbers are numbers with exactly $2$ factors.

A prime number's only factors are $\greenD1$ and the number $\purpleD{\text{itself}}$.

$7$ is an example of a prime number. Its only factors are $\greenD1$ and $\purpleD7$. It is not evenly divisible by any other whole numbers.

[[☃ explanation 1]]

Want to learn more about prime numbers? Check out this video.

##Practice set 1: Identifying prime numbers

[[☃ graded-group-set 1]]

Want to try more problems like this? Check out this exercise.

##What are composite numbers?

Composite numbers have more than $2$ factors. A composite number has factors in addition to $1$ and the number $\text{itself}$.

$16$ is an example of a composite number. The factors of $16$ are $1, 2, 4, 8$ and $16.$ All of these numbers divide into $16$ evenly.

Want to learn more about recognizing prime and composite numbers? Check out this video.

Want more ways to think about prime and composite numbers? Check out this article.

##Practice set 2: Identifying composite numbers

[[☃ graded-group-set 1]]

Want to try more problems like this? Check out this exercise.