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| − | 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.
| + | #REDIRECT[[Divisor function]] |
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| − | Example: Count the divisors of 72.
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| − | Soulution: <math>72=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.
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| − | 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.
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| − | ==See Also==
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| − | *[[Number theory]]
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| − | *[[Counting]]
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| − | *[[Divisor]]
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