Multiple (mathematics)

From Infogalactic: the planetary knowledge core
Jump to: navigation, search

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:

  •   14 = 7 \times 2
  •   49 = 7 \times 7
  •  -21 = 7 \times (-3)
  •    0 = 7 \times 0
  •    3 = 7 \times (3/7), 3/7 is a rational number, not an integer
  •   -6 = 7 \times (-6/7), -6/7 is a rational number, not an integer.

Properties

  • 0 is a multiple of everything (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 and a-b are also multiples of x.

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