# Multiple (mathematics)

In mathematics, a **multiple** is the product of any quantity and an integer.^{[1]}^{[2]}^{[3]} In other words, for the quantities *a* and *b*, we say that *b* is a multiple of *a* if *b* = *na* for some integer *n*, which is called the multiplier or coefficient. If *a* is not zero, this is equivalent to saying that *b*/*a* is an integer with no remainder.^{[4]}^{[5]}^{[6]} If *a* and *b* are both integers, and *b* is a multiple of *a*, then *a* is called a divisor of *b*.

## Contents

## Examples

14, 49, -21 and 0 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:

- , is a rational number, not an integer
- , is a rational number, not an integer.

## Properties

- 0 is a multiple of everything ().
- The product of any integer and any integer is a multiple of . In particular, , which is equal to , is a multiple of (every integer is a multiple of itself), since 1 is an integer.
- If and are multiples of then and are also multiples of .

## References

- ↑ Weisstein, Eric W., "Multiple",
*MathWorld*. - ↑ WordNet lexicon database, Princeton University
- ↑ WordReference.com
- ↑ The Free Dictionary by Farlex
- ↑ Dictionary.com Unabridged
- ↑ Cambridge Dictionary Online