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Lesson 2: Prime and composite numbers

# Prime and composite numbers intro

Learn about prime and composite numbers and practice identifying them.

## 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.
$15÷1=15$
$15÷3=5$
$15÷5=3$
$15÷15=1$
$15$ has four factors: $1,3,5$, and $15$.
Problem 1A
Which of the following numbers are factors of $17$?

All numbers have $1$ and $\text{themselves}$ as factors.
$3÷1=3$
$3÷3=1$

## 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 $1$ and the number $\text{itself}$.
$7$ is an example of a prime number. Its only factors are $1$ and $7$. 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.
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.
Problem 2A
Is $13$ a prime number?

## 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.
He could also have $2$ rows with $8$ eggs in each row.
Or he could have $4$ rows with $4$ eggs in each row.
Composite numbers have more than one way that they can be divided into equal groups.
Problem 3A
Is $15$ a composite number?

### The number $1$‍

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

## Practice with prime and composite numbers

Problem 4A
The numbers $11,17,$ and $23$ are all
numbers.

## Prime number and composite number challenge

Use the clues given to solve the problems below.
Problem 5A
Identify a prime number with $5$ in the ones place.