Multiple (mathematics).html

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.

Examples

14, 49, 0 and -21 are multiples of 7 where as 3 and -6 are not.

Multiples:

6 → 3,2

12 → 4,3,2,6,12

Properties

Every integer is a multiple of itself ( $b=1\cdot b$ ).
0 is a multiple of every integer ( $0=0\cdot b$ ).
A multiple of an integer is obtained by multiplying the integer 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).

Multiple (mathematics).html

Examples

Properties

See also