Factors and Roots Doubts

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Cud someone explain this theory? Like how GRE could trick us?

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Over here we wud just take the LCM right I dont find any other way

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How do I find the no of odd and even factors

It is just trying to tell us that \sqrt{4} can be +2 or -2, while the cube root of 8 is only 2. That is, if t is positive,

a^{1/t} has two values if t is even, and one if t is odd.

That’s one way.

36 = 2^2 \times 3^2

For a factor to be odd you need to consider only the odd terms. In this case, 3. For even, you can consider (total number of factors - odd factors).

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Thanks a lot