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In mathematics, a multiple is the product of any quantity and an integer. 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. If a and b are both integers, and b is a multiple of a, then a is called a divisor of b.
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.
- 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 .
- Weisstein, Eric W., "Multiple", MathWorld.
- WordNet lexicon database, Princeton University
- The Free Dictionary by Farlex
- Dictionary.com Unabridged
- Cambridge Dictionary Online