MULTIPLE (MATHEMATICS)

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 $a=nb,$ where $n$ is an integer. If $b$ is not zero, this is equivalent to saying that $a/b$ is an integer.

Contents

Examples

Properties

See also

Examples

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

Properties

★ Every number is a multiple of itself ($b=1cdot\; b$).

★ 0 is a multiple of every number ($0=0cdot\; b$).

★ If $a$ and $b$ are multiples of $x,$ then $a+b$, $a-b$ and $ab$ 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).
72 is a mutliple of 36!

See also

★ Ideal (ring theory)

★ Decimal and SI prefix