Difference between revisions of "Multiple"
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| − | A '''multiple''' of a given [[integer]] is the product of that integer with some other integer. Thus <math>k</math> is a multiple of <math>m</math> exactly when <math>k</math> can be written in the form <math>nm</math> where <math>n</math> and <math>m</math> are integers. (In this case, <math>k</math> is a multiple of <math>n</math>, as well). Every integer has an [[infinite]] number of multiples. As an example, a few of the multiples of 15 are 15, 30, 45, 60, and 75. A few of the multiples of 3 are 3, 6, 9, 12, and 15. | + | A '''multiple''' of a given [[integer]] is the product of that integer with some other integer. Thus <math>k</math> is a multiple of <math>m</math> exactly when <math>k</math> can be written in the form <math>nm</math> where <math>n</math> and <math>m</math> are integers. (In this case, <math>k</math> is a multiple of <math>n</math>, as well). |
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| + | Every nonzero integer has an [[infinite]] number of multiples. As an example, a few of the multiples of 15 are 15, 30, 45, 60, and 75. A few of the multiples of 3 are 3, 6, 9, 12, and 15. | ||
An equivalent phrasing is that <math>k</math> is a multiple of <math>m</math> exactly when <math>k</math> is [[divisibility | divisble by]] <math>m</math>. | An equivalent phrasing is that <math>k</math> is a multiple of <math>m</math> exactly when <math>k</math> is [[divisibility | divisble by]] <math>m</math>. | ||
Revision as of 08:15, 19 April 2008
A multiple of a given integer is the product of that integer with some other integer. Thus 
is a multiple of 
exactly when can be written in the form 
where 
and are integers. (In this case, is a multiple of , as well).
Every nonzero integer has an infinite number of multiples. As an example, a few of the multiples of 15 are 15, 30, 45, 60, and 75. A few of the multiples of 3 are 3, 6, 9, 12, and 15.
An equivalent phrasing is that is a multiple of exactly when is divisble by .
