Multiple
An integer [latex]N[/latex] is a multiple of an integer [latex]n[/latex] if there is an integer [latex]a[/latex] for which [latex]N = n × a[/latex].
If the number [latex]N[/latex] is a multiple of a non-zero number [latex]n[/latex], then the number [latex]n[/latex] is a divisor of the number [latex]N[/latex].
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.
Symbol
The symbol "mult([latex]n[/latex])" is read as "the multiples of [latex]n[/latex]".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, …}.