Difference between revisions of "Divisor"
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===Definition=== | ===Definition=== | ||
− | Any [[natural number]] <math>\displaystyle{d}</math> is called a divisor of a natural number <math>\displaystyle{n}</math> if there is a natural number <math>\displaystyle{k}</math> such that <math>n=kd</math> or, in other words, if <math>\displaystyle\frac nd</math> is also a natural number. | + | Any [[natural number]] <math>\displaystyle{d}</math> is called a divisor of a natural number <math>\displaystyle{n}</math> if there is a natural number <math>\displaystyle{k}</math> such that <math>n=kd</math> or, in other words, if <math>\displaystyle\frac nd</math> is also a natural number. See [[Divisibility]] for more information. |
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+ | === Notation=== | ||
+ | A common notation to indicate a number is a divisor of another is n|k. This means that n divides k. | ||
===How many divisors does a number have=== | ===How many divisors does a number have=== | ||
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*[[Number theory]] | *[[Number theory]] | ||
*[[GCD]] | *[[GCD]] | ||
+ | *[[Divisibility]] |
Revision as of 11:39, 21 June 2006
Contents
[hide]Definition
Any natural number is called a divisor of a natural number
if there is a natural number
such that
or, in other words, if
is also a natural number. See Divisibility for more information.
Notation
A common notation to indicate a number is a divisor of another is n|k. This means that n divides k.
How many divisors does a number have
See main article, Counting divisors. If is the prime factorization of
, then the number
of different divisors of
is given by the formula
. It is often useful to know that this expression grows slower than any positive power of
as
. Another useful idea is that
is odd if and only if
is a perfect square.
Useful formulae
- If
and
are relatively prime, then