MathematicsFor a positive integer n  , define d(n)=  number of positive divisors of n  . What is the value of d[d(d(12))]?  

For a positive integer n  , define d(n)=  number of positive divisors of n  . What is the value of d[d(d(12))]?  


  1. A
    3
  2. B
    4
  3. C
    5
  4. D
    6 

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    Solution:

    Consider the given question,
    For a positive integer n  , define d(n)=  number of positive divisors of n  .
    We know that,
    Positive Divisors: The divisors of a positive integer are the integers that evenly divide it.
    Divisors of 12 are 1,2,3,4,6,12.
    n=   number of positive divisors of 12 is 6.  d(12)=6  
    Divisors of 6 are 1,2,3,6.
    n=   number of positive divisors of 6 is 4.
    d(6)=4  
    Divisors of 4 are 1,2,4.
    n=   number of positive divisors of 4 is 3.
    d(4)=3  
    The value of d d d 12   ,
    d[d(d(12))] =d[d(6)] d[d(d(12))] =d[4] d[d(d(12))] =3  { d(12)=6,d(6)=4,d(4)=3   }
    Hence, the value of d d d 12  is 3.
    Therefore, option 1 is correct.
     
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