A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers W are possible?  Choose the most appropriate option:  A) 2  B) 4  C) 6  D) 3  E) Not possible
Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2   Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total W of 6 possibilities.   6.
<result>C</result>
A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers W are possible?