**Prime** numbers have exactly 2 factors – just 1 and itself.

Some of the smallest prime numbers are 1-digit numbers.

- 3 is a
**prime number.**

- 5 is a
**prime number.**

- 7 is a
**prime number.**

3, 5, & 7 are **prime** because they cannot be divided evenly into equal groups.

let’s go over a few special cases of prime numbers.

**0**is not prime or composite.- When 0 is used as a place holder in the ones place, though, it makes a number even so it is automatically composite.

**1**is not prime or composite either.- The definition of prime says a number has “exactly 2 factors.” 1 only has 1 factor – itself!

**2**is a prime number.- It is the only even prime number, because it only has 2 factors – 1 & itself.

All **prime numbers** (except for 2!) are **odd**.

But, **not all odd numbers are prime**.

**How to identify if a number is prime**

- Test if it is divisible by any other numbers.
- Find its factors.

The first 9 prime numbers are highlighted below. Each number is only divisible by 1 & itself.

**2** is prime. It is only divisible by 1 & itself.

- 2 ÷ 2 = 1
- 2 ÷ 1 = 2

Factors of 2: 2 & 1

**3** is prime. It is only divisible by 1 & itself.

- 3 ÷ 3 = 1
- 3 ÷ 1 = 3

Factors of 3: 3 & 1

**5** is prime. It is only divisible by 1 & itself.

- 5 ÷ 5 = 1
- 5 ÷ 1 = 5

Factors of 5: 5 & 1

## Divisibility Rules

Every number that meets any of the **divisibility rules** from 2 down *(except for 2)* is composite.

Divisible by? | Rule |
---|---|

1 | Every number is divisible by 1 and itself. |

2 | Every even number (with 0, 2, 4, 6, or 8 ones) is divisible by 2. |

3 | The sum of the number’s digits will be divisible by 3: 3, 6, 9, etc. |

4 | Use strategies to check for divisibility by 4. Every other even number from 4 is divisible by 4. |

5 | Numbers that end in 5 or 0 are divisible by 5. |

6 | Numbers are divisible by 6 if they are divisible by 2 AND 3. |

7 | Use strategies to check for divisibility by 7. |

8 | Use strategies to check for divisibility by 8. |

9 | The sum of the number’s digits will be divisible by 9. |

10 | Numbers with 0 ones are divisible by 10. |

**Is 9 prime?**

Can 9 be divided into equal groups?

Yes, 9 ÷ 3 = 3

The factors of 9 are 1, 3, & 9.

9 is a multiple of 3 x 3, so **9 is a composite number**.

**Is 24 prime?**

No.

24 is even & divisible by 2.

24 ÷ 2 = 12

24 is a composite number.

**Is 31 prime?**

Yes! 31 is prime.

- 31 is odd, so it isn’t divisible by 2.
- 3 + 1 = 4, so it isn’t divisible by 3.
- It’s not divisible by 4 because 4 x 7 = 28 and 4 x 8 = 32.
- It’s not divisible by 5 or 10 because there is only 1 one.
- It’s not divisible by 6 because 6 x 5 = 30 and 6 x 6 = 36.
- It’s not divisible by 7 because 7 x 4 = 28 and 7 x 5 = 35.
- It’s not divisible by 8 because 8 x 3 = 24 and 8 x 4 = 32.
- It’s not divisibly by 9 because 9 x 3 = 27 and 9 x 4 = 36.

## Practice Problems

**True or False? **

The number **21** is odd, so it’s a prime number.

21 is composite.

21 is composite.

21 is a **multiple** of 3 and 7.

Its **factors** are 1, 3, 7, & 21.

Select the prime numbers.

Select the prime numbers.