# 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.