# Multiple

## Multiple

An integer $$N$$ is a multiple of an integer $$n$$ if there is an integer $$a$$ for which $$N = n × a$$.

If the number $$N$$ is a multiple of a non-zero number $$n$$, then the number $$n$$ is a divisor of the number $$N$$.

### Properties

• All integers are multiples of 1 and themselves: 7 = 7 × 1.
• The number 0 is considered to be a multiple of all integers n, because: 0 = 0 × n, is not the divisor of any integer.

In a specific context, the list of the lowest multiples of an integer is called the table of this number. This means that we can talk about the table of 9, for example.

### Symbol

The symbol “mult($$n$$)” is read as “the multiples of $$n$$“.

### Examples

• The set of the positive multiples of 6 is: mult(6) = {6, 12, 18, 24, 30, 36, 42, …}.
• The set of the multiples of 6 is: mult(6) = {…, –30, –24, –18, –12, –6, 0, 6, 12, 18, 24, 30, …}.