AskDefine | Define submultiple

User Contributed Dictionary

English

Noun

  1. An integer that is an exact divisor or another

Translations

submultiple
  • Italian: sottomultiplo

Extensive Definition

In mathematics, a multiple of an integer is the product of that integer with another integer. In other words, a is a multiple of b if a=nb, where n is an integer. If b is not zero, this is equivalent to saying that a/b is an integer.

Examples

  • 14, 49, and 21 are multiples of 7 whereas 3, 15, and 20 are not.

Properties

  • Every number is a multiple of itself (b=1\cdot b ).
  • 0 is a multiple of every integer (0=0\cdot b ).
  • A multiple of a number is obtained by multiplying the number by any natural number.
  • If a and b are multiples of x, then a+b, a-b and ab are multiples 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).
submultiple in Bulgarian: Кратно
submultiple in Spanish: Múltiplo
submultiple in Hungarian: Szorzás
submultiple in Korean: 배수
submultiple in Japanese: 倍数
submultiple in Polish: Wielokrotność
submultiple in Swedish: Multipel
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