rx10 wrote:
Factors of \(344 ( 2 * 2 * 2 * 43 ) = 1 , 2 , 4 , 8 , 43 , 86 , 172 , 344\)
No of odd factors : \(2\) & no of even factors : \(6\)
A difference between the numbers of odd and even factors \(= 2 - 6 = -4\)
Multiply by \(\frac{1}{2}\) \(= \frac{-4}{2} = -2\)
Answer B
Great, thanks for solution. My only worry is that with bigger number, say not 344 but 687 or something different, listing the odd and the even may be time consuming. Therefore, I offer to separate these two categories such as \(2^3 * 43\) and the number of positive factors will be \((3+1)*(1+1)\). While the number of odd factors is simply \((1+1)\), the remaining will be even factors \(8-2=6\).
I have also updated the question's prompt as factors sought here are positive only. This is my made question. I have GRE in less than 10 days (6th August). Fingers crossed, as I hope to attain at least Q160