# Multiples

A number, **a,** is a **multiple** of another number, **b**, when the result of** multiplying it **is another number, **c**.

**a = b · c**

18 is a multiple of two, since it is the result of multiplying 2 by 9.

18 = 2 · 9

A natural multiple is obtained when a natural number is multiplyed by another natural number.

#### Multiples of 2

2 · 0 = 0 |
2 · 1 = 2 |
2 · 2 = 4 |
2 · 3 = 6 |
2 · 4 = 8 |

2 · 5 = 10 |
2 · 6 = 12 |
2 · 7 = 14 | 2 · 8 = 16 |
2 · 9 = 18 |

#### Multiples of 3

3 · 0 = 0 |
3 · 1 = 3 |
3 · 2 = 6 |
3 · 3 = 9 |
3 · 4 = 12 |

3 · 5 = 15 |
3 · 6 = 18 |
3 · 7 = 21 |
3 · 8 = 24 |
3 · 9 = 27 |

#### Multiples of 4

4 · 0 = 0 |
4 · 1 = 4 |
4 · 2 = 8 |
4 · 3 = 12 |
4 · 4 = 16 |

4 · 5 = 20 |
4 · 6 = 24 |
4 · 7 = 28 |
4 · 8 = 32 |
4 · 9 = 36 |

#### Multiples of 5

5 · 0 = 0 |
5 · 1 = 5 |
5 · 2 = 10 |
5 · 3 = 15 |
5 · 4 = 20 |

5 · 5 = 25 |
5 · 6 = 30 |
5 · 7 = 35 |
5 · 8 = 40 |
5 · 9 = 45 |

## Properties of the Multiples of a Number

1 Any number, except 0, is **a multiple** of itself and one.

2 Zero is a **multiple** of all numbers.

3Any number, except zero, has ** infinite multiples**.

4 If a number, **a**, is** a multiple of** **b**, the division between a and b is exact.

5 The **sum** of several **multiples** of a number is another** multiple of** that number.

6 The **difference** of two** multiples **of a number is another** multiple of** that number.

7If a number is a multiple of another, and this number is a multiple of a third one, the first number is a multiple of the third one.

8 If a number is a multiple of another, all the** multiples** of the first number are also multiples of the second.