Bunuel wrote:
If w, x, y and z are integers such that 1 < w ≤ x ≤ y ≤ z and wxyz = 924, then how many possible values exist for z?
(A) Three
(B) Four
(C) Five
(D) Six
(E) Seven
We can break 924 into prime factors:
924 = 3 x 308 = 3 x 4 x 77 = 3 x 2 x 2 x 11 x 7
We see that 924 is a product of 5 (not necessarily distinct) prime factors. If we want to express 924 as a product of 4 factors (each of which is greater than 1), one of the factors must be the product of two of 5 prime factors. Since
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