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# NumTheSL5#16

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May 28, 2019

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The number 12 can be broken up to $$x^2*y^2$$, since the number of factors is $$(2+1)(2+1)=3\cdot3=9.$$ The three numbers do not work here since there are no possible outcomes.

Thus, we can have: $$2^2*3^2=36.$$

$$2^2*5^2=100.$$

$$2^2*7^2=196.$$

I do not think any more possible outcomes are there, and you can still check my work.

Thus, the answer is $$36+100+196=\boxed{332}.$$

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May 28, 2019