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.

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

1. ↑ Weisstein, Eric W. "Multiple". MathWorld. 
2. ↑ WordNet lexicon database, Princeton University
3. ↑ WordReference.com
4. ↑ The Free Dictionary by Farlex
5. ↑ Dictionary.com Unabridged
6. ↑ Cambridge Dictionary Online

See also

• Ideal (ring theory)
• Decimal and SI prefix