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:<math>(3 + 1) * (1 + 1) = 8</math>
:<math>(3 + 1) * (1 + 1) = 8</math>
and they are 1, 2, 3, 4, 6, 8, 12, and 24.
and they are 1, 2, 3, 4, 6, 8, 12, and 24. It's easy to see why this formula works. Suppose, for example, that n = 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup>. Then the factors of n are exactly the numbers 2<sup>j</sup> 3<sup>k</sup> 5<sup>l</sup>, where j is between 0 and a, k is between 0 and b, and l is between 0 and c. So the number of factors is just the number of choices for j, times the number of choices for k, times the number of choices for l, which is (a+1)(b+1)(c+1).
==Other uses==
==Other uses==