Question

. What are the total number of divisors of 600(including 1 and 600)?

Answer 1

There are a total of 24 divisors of 600 , including 1 and 600.
They are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300 and 600. 

Answer 2

We can do this in some other ways other than listing the all factors.

1.  First find square root (600) = 24.5     There are always as many factors less
      than square root as more than it.     The factors less than 24.5 are :

                1,2,3,4,5,6,8,10,12,15,20,24.

     there are 12 of them.   so above 24.5 ther are 12.
         so total number of factors = 24


2. 600 = 2^3 * 3^1 * 5^2

     A factor is formed by selecting one 2 or two 2s or three 2s or no 2s.  Also by      selecting no 3s or one 3.    finally,  no 5 may be chosen, 1 or two 5s may be      chosen to form a factor.

      so number ways of forming a factor = 4 * 2 * 3 = 24

                  so 24 factors.