Counting divisors
Revision as of 22:42, 19 June 2006 by IntrepidMath (talk | contribs)
Counting divisors means to find out how many numbers divide a main number. Note that the number itself and the number 1 must be counted. This is easy to explain with an example.
Example: Count the divisors of 72.
Soulution: 
. 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.
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. 
where each of the 
are the exponents of the nth unique exponentiation base.
