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## Understanding Prime Numbers

#### Introduction

A Prime Number is a number that cannot be evenly divided by any other whole number other than 1 and itself. So 1, 2, 3 and 5 are all prime numbers, but 4 is not, since 4 can not only be divided by 1 and 4, but 2 as well.

#### Terms

**Prime Number**- A prime number is a number that cannot be evenly divided by any number other than 1 and itself.

## Lesson

A prime number is a number that is not evenly divisible by any number other than 1 or itself. So if we are asked to list all the prime numbers between 1 and 10, we could determine the answer by considering each number between 1 and 10, and determining whether it has any factors other than 1 and itself.

Essentially, any number that has an entry in the 'Other Factors' column is not a prime factor. So the prime numbers between 1 and 10 are 1, 2, 3, 5 and 7.

(Fun Fact: Did you know that '2' is the only even prime number?)

## Examples

#### Picking Prime Numbers

Which of the whole numbers $23, 25, 27\text{ and }29$ are prime numbers?

The factors of $23$ are $1\text{ and }23$. Therefore $23$ is a prime number.

The factors of $25$ are $1, 5\text{ and }25$. Therefore $25$ is not a prime number.

The factors of $27$ are $1, 3, 9\text{ and }27$. Therefore $27$ is not a prime number.

The factors of $29$ are $1\text{ and }29$. Therefore $29$ is a prime number.

#### Listing Prime Numbers

List prime numbers between $5$ and $12$

$5, 7\text{ and }11$ are the prime numbers between $5$ and $12$

#### Picking Prime Numbers

Which of the whole numbers $35, 37, 39\text{ and }41$ are prime numbers?

The factors of $35$ are $1, 5, 7\text{ and }35$. Therefore $35$ is not a prime number.

The factors of $37$ are $1\text{ and }37$. Therefore $37$ is a prime number.

The factors of $39$ are $1, 3, 13\text{ and }39$. Therefore $39$ is not a prime number.

The factors of $41$ are $1\text{ and }41$. Therefore $41$ is a prime number.

#### Listing Prime Numbers

List prime numbers between $20$ and $30$

$23\text{ and }29$ are the prime numbers between $20$ and $30$

#### Picking Prime Numbers

Which of the whole numbers $35, 41, 47\text{ and }49$ are prime numbers?

The factors of $35$ are $1, 5, 7\text{ and }35$. Therefore $35$ is not a prime number.

The factors of $41$ are $1\text{ and }41$. Therefore $41$ is a prime number.

The factors of $47$ are $1\text{ and }47$. Therefore $47$ is a prime number.

The factors of $49$ are $1, 7\text{ and }49$. Therefore $49$ is not a prime number.