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. | + | 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> only if <math>k</math> can be written in the form <math>mn</math>, where <math>m</math> and <math>n</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, some of the multiples of 15 are 15, 30, 45, 60, and 75. | ||
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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>. | ||
| + | In Modular Arithmetic, multiples of the modulus, are congruent to 0 | ||
== See also == | == See also == | ||
| + | *[[Common multiple]] | ||
*[[Least common multiple]] | *[[Least common multiple]] | ||
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| + | [[Category:Number theory]] | ||
Revision as of 18:21, 26 February 2020
A multiple of a given integer is the product of that integer with some other integer. Thus 
is a multiple of 
only if 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, some of the multiples of 15 are 15, 30, 45, 60, and 75.
An equivalent phrasing is that is a multiple of exactly when is divisble by .
In Modular Arithmetic, multiples of the modulus, are congruent to 0
