For all positive integers f, f◎ equals the distinct pairs of positive integer factors. For example, 16◎ =3, since there are three positive integer factor pairs in 16: 1 x 16, 2 x 8, and 4 x 4.
What is the greatest possible value for f◎ if f is less than 100? Choose the correct choice from the following answers:	A) 6	B) 7	C) 8	D) 9	E) 10
I took numbers in reverse order from 99 and got 6 distinct pairs in 96.   I thought it may be because 96=(2^5*3) has   (5+1)*(1+1)= 
<gadget id="calculator">  (5+1)*(1+1)</gadget>
<output>12</output>
12(perhaps maximum) factors.   1*96,2*48*4*24,8*12,16*6,32*3   However, I was not sure while answering this. Please let us know if there is a better way.   6ns: "6"
<result>A</result>
For all positive integers f, f◎ equals the distinct pairs of positive integer factors. For example, 16◎ =3, since there are three positive integer factor pairs in 16: 1 x 16, 2 x 8, and 4 x 4.
What is the greatest possible value for f◎ if f is less than 100?