All factors of a positive integer X are multiplied and the product obtained is X^3. If X is greater than 1, how many factors does X have? Choose one:  A) 2  B) 3  C) 4  D) 5  E) 6
The question can be done in seconds if you understand the properties of factors of a number. Note that every distinct factor of a number which is not a perfect square has a complementary factor.   For example,   Factors of 6: 1, 2, 3, 6   1 has a complementary factor 6 such that   1*6= 
<gadget id="calculator">  1*6</gadget>
<output>6</output>
6 (the original number)   2 has a complementary factor 3 such that   2*3= 
<gadget id="calculator">  2*3</gadget>
<output>6</output>
6 (the original number)   So if you have a number, n, which is not a perfect square, and start multiplying its factors, you will get n to a certain power. the power will half of the number of factors. For example, 6 has 4 factors and when you multiply all 4 factors, you get 6^2 (2 is half of 4).   So if you know that the product of all factors is X^3, it means there must have been twice the number of factors i.e. 3*2= 6 factors.   6)
<result>E</result>
All factors of a positive integer X are multiplied and the product obtained is X^3. If X is greater than 1, how many factors does X have?