How do you find the number of factors of a number?

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Answer 1 · 2016-03-13T05:44:36

If the prime factorization of $n \in N$ $n∈N$ is

$n = \prod k = 1 p_{k}^{a_{k}}$ $n=\prod_{k=1} p_k^{a_k}$

then the number of divisors of $n$ $n$ is

$\prod k = 1 (a_{k} + 1)$ $\prod_{k=1} (a_k+1)$

For example $36 = 3^{2} \cdot 2^{2}$ $36=3^2*2^2$ the number of divisors is

$(2 + 1) \cdot (2 + 1) = 9$ $(2+1)*(2+1)=9$

which are

$1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 36$ $1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 36$