Multiple (mathematics)

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In mathematics, a multiple of an integer is the product of that integer with another integer. In other words, a is a multiple of b if $a = n b,$ where $n$ is an integer. If $b$ is not zero, this is equivalent to saying that $a / b$ is an integer.

[edit] Examples

14, 49, and 21 are multiples of 7 whereas 3, 15, and 20 are not.

[edit] Properties

Every number is a multiple of itself ( $b=1\cdot b$ ).
0 is a multiple of every integer ( $0=0\cdot b$ ).
A multiple of a number is obtained by multiplying the number by any natural number.
If $a$ and $b$ are multiples of $x,$ then $a + b$ , $a - b$ and $a b$ are multiples of $x .$
For any integer $p > 1,$ $(p - 1)! + 1$ is a multiple of $p$ if and only if $p$ is a prime number (Wilson's theorem).