Difference between revisions of "Counting divisors"

Latest revision as of 09:36, 29 July 2006

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-The general task of '''counting divisors''' of any [[integer]] requires us to ''organize'' the [[divisor | divisors]] of an integer.  The [[prime factorization]] of the integer gives us a way to describe, and therefore organize, these divisors.
+#REDIRECT[[Divisor function]]
-== Example: 72 ==
-Consider the task of counting the divisors of 72.<br>
-<math>\displaystyle72=2^{3} \cdot 3^{2}.</math>
-Since each divisor of 72 can have a power of 2, and since this power can be 0, 1, 2, or 3, we have 4 possibilities. Likewise, since each divisor can have a power of 3, and since this power can be 0, 1, or 2, we have 3 possibilities. By an elementary [[counting]] principle, we have 3*4='''12''' divisors.
-== Formula ==
-Generally, If we have a number's prime factorization, the number of divisors is equal to the product of each of the exponents plus one, i.e. <math>(e_1+1)(e_2+1)\ldots(e_n+1)</math> where each of the <math>e_i</math> are the exponents of the nth unique exponentiation base.
-==See Also==
-*[[Number theory]]
-*[[Counting]]
-*[[Divisor]]