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

[edit] Examples

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

[edit] Properties

Every number is a multiple of itself (<math>b=1\cdot b </math>).
0 is a multiple of every number (<math>0=0\cdot b</math>).
If <math>a</math> and <math>b</math> are multiples of <math>x,</math> then <math>a+b</math>, <math>a-b</math> and <math>ab</math> are multiples of <math>x.</math>
For any integer <math> p > 1,</math> <math>(p-1)!+1</math> is a multiple of <math>p</math> if and only if <math>p</math> is a prime number (Wilson's theorem).