Multiple (mathematics)

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

Examples

14, 49, 0 and -21 are multiples of 7 whereas 3 and -6 are not. This is because there are integers that 7 may be multiplied by to reach the values of 14, 49, 0, and -21, while there are no such integers for 3 and -6. Each of the products listed below, and in particular, the products for 3 and -6, is the only way that the relevant number can be written as a product of 7 and another real number:

• $14=7\times 2$;
• $49=7\times 7$;
• $0=7\times 0$;
• $-21=7\times (-3)$;
• $3=7\times (3/7)$, and $3/7$ is a fraction, not an integer; and
• $-6=7\times (-6/7)$, and $-6/7$ is a fraction, not an integer.

Properties

• 0 is a multiple of every integer ($0=0\cdot b$).
• The product of any integer $n$ and any integer is a multiple of $n$. In particular, $n$, which is equal to $n\times 1$, is a multiple of $n$ (every integer is a multiple of itself), since 1 is an integer.
• If $a$ and $b$ are multiples of $x,$ then $a+b$, $a-b$ and $ab$ are multip you can fuck me les 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).

See also

• Divisor
• Ideal (ring theory)
• Decimal and SI prefix

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