2017 UNCO Math Contest II Problems/Problem 11
Problem
Divide and Conquer
(a) How many different factorizations are there of (which is ) in which each factor is either a square or a cube (or both) of an integer and each factor is greater than one? Regard and as the same factorization: the order in which the factors are written does not matter. Regard the number itself, , as one of the factorizations.
(b) How many different factorizations are there of as a product of factors in which each factor is either a square or a cube (or both) of an integer and each factor is greater than one? As before, the order in which the factors is written does not matter, and the number itself counts as a factorization. Note that = .
Solution
(a) 16
(b) 42
See also
2017 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
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Followed by last question | |
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All UNCO Math Contest Problems and Solutions |